Basic Ratios Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB)

Soru 1Soru →

A mechanical winch uses a gear system where the driving gear and the driven gear have a revolution ratio of $4:7$ . If the driving gear completes $124$ revolutions during a lifting operation, how many revolutions does the driven gear complete?

Cevabı ve açıklamayı göster

Cevap: 217

Cevap

217

The correct answer is found by setting up a direct proportion based on the 4:7 ratio. Since the driving gear's 4 parts scale up to 124 actual revolutions, the scale factor is 31 (124 ÷ 4). Multiplying the driven gear's 7 parts by this same scale factor yields 217 revolutions.

Adım Adım Çözüm

1

Identify the known ratio

Driving : Driven = 4 : 7

This establishes the proportional relationship between the two gears.

2

Set up a proportion using the known quantity

4 / 7 = 124 / x

We know the driving gear completes 124 revolutions, which corresponds to the '4' in the ratio.

3

Find the scale factor

124 ÷ 4 = 31

This tells us how many times greater the actual operation is compared to the base ratio.

4

Calculate the unknown quantity

7 × 31 = 217

Applying the same scale factor to the driven gear maintains the proportional relationship.

Anahtar Kavram

Solving for an unknown part in a part-to-part relationship using scale factors.

Soru 2Soru →

During a ship repair project, a naval shipyard assigns 24 welders and 8 pipefitters to complete the structural work. What is the ratio of welders to pipefitters on this project, expressed in its simplest form?

3:1

1:3

3:4

1:4

Cevabı ve açıklamayı göster

Cevap: 3:1

Cevap

3:1

The correct answer accurately extracts the given quantities (24 welders, 8 pipefitters), sets them up in the requested sequence (24 to 8), and successfully reduces the numbers to their simplest terms by dividing both by 8, yielding 3:1.

Adım Adım Çözüm

1

Identify the two quantities that need to be compared based on the question.

Welders = 24, Pipefitters = 8

The question asks for the specific ratio of welders to pipefitters.

2

Set up the initial ratio in the exact order requested by the problem.

24:8

The order of terms in a ratio matters; it must strictly match 'welders to pipefitters'.

3

Simplify the ratio by dividing both numbers by their greatest common divisor (GCD).

The GCD of 24 and 8 is 8. Therefore, (24 ÷ 8) : (8 ÷ 8) = 3:1

Ratios are conventionally expressed in their lowest possible integer terms.

Anahtar Kavram

Basic Ratios

Tahmini Süre:45s

Soru 3Soru →

Match each military supply and maintenance inventory count to its correctly simplified ratio.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct matches pair each scenario to its mathematically simplified ratio.

Each correct match is found by writing the quantities in the requested order and then dividing all terms by their greatest common factor.

Adım Adım Çözüm

1

Identify the quantities to be compared in the exact order requested by each scenario.

The numerical values are extracted in the correct sequence.

Ratios represent a specific relationship, and the order of the terms must match the order requested in the text.

2

Write the initial unsimplified ratios for all scenarios.

The initial ratios are

24:8

,

10:15

,

20:5

, and

10:5:15

.

This establishes the mathematical baseline before simplification.

3

Find the greatest common factor (GCF) for the numbers in each ratio and divide.

The simplified ratios are

3:1

,

2:3

,

4:1

, and

2:1:3

.

Ratios should always be expressed in their simplest terms.

Anahtar Kavram

Basic Ratios and Simplification

Soru 4Soru →

A technician spends $2$ hours diagnosing a communications system and $30$ minutes completing the repair. What is the ratio of the time spent diagnosing to the time spent repairing?

4:1

1:15

1:4

4:5

Cevabı ve açıklamayı göster

Cevap: $4:1$

Cevap

The correct ratio is

4:1

.

To find the correct ratio, both times must be expressed in the same unit. Converting

2

hours gives

120

minutes. The requested ratio of diagnosing time to repairing time is

120:30

. Dividing both numbers by their greatest common divisor (

30

) yields the simplest form,

4:1

.

Adım Adım Çözüm

1

Convert the diagnosing time to the same unit as the repair time.

2

hours =

2 \times 60

minutes =

120

minutes.

Ratios must compare quantities in the same units to be mathematically meaningful.

2

Set up the ratio of diagnosing time to repair time.

120

minutes :

30

minutes

The question specifically asks for the ratio of diagnosing time first, followed by repair time.

3

Simplify the ratio to its lowest terms.

120 : 30 = 4 : 1

Divide both parts of the ratio by their greatest common divisor, which is

30

.

Anahtar Kavram

To find a ratio between two real-world quantities, ensure they share the same units, express their relationship in the exact order requested, and simplify.

Soru 5Soru →

A military dining facility prepares a standard meal using a ratio of $4$ pounds of beef for every $3$ pounds of rice. If the facility uses $24$ pounds of rice for a meal, how many pounds of beef will be needed?

Cevabı ve açıklamayı göster

Cevap: 32

Cevap

32

Because the required ratio of beef to rice is

4:3

, every

3

pounds of rice requires

4

pounds of beef. Since

24

pounds of rice is

8

times the base amount (

24 \div 3 = 8

), the amount of beef must also be scaled by

8

. Multiplying

4

pounds by

8

yields exactly

32

pounds of beef.

Adım Adım Çözüm

1

Identify the given ratio and the known actual quantity.

The ratio of beef to rice is

4:3

. The actual amount of rice used is

24

pounds.

Establishing the known values is the first step in solving a proportion.

2

Determine the scale factor between the base ratio and the actual amounts.

24 \div 3 = 8

. The scale factor is

8

.

Since the ratio amount for rice is

3

and the actual amount is

24

, multiplying by

8

scales the ratio up to the actual meal size.

3

Apply the scale factor to the beef portion of the ratio to find the missing quantity.

4 \times 8 = 32

.

To maintain the exact proportional relationship, both parts of the ratio must be multiplied by the same scale factor.

Anahtar Kavram

Solving for a missing quantity in a part-to-part ratio using a scale factor.

Tahmini Süre:1m 0s

Soru 6Soru →

A military logistics unit is preparing a supply drop. The standard loadout requires a ratio of $2$ pallets of Meals Ready-to-Eat (MREs) for every $3$ pallets of bottled water. If the unit loads $30$ pallets of MREs, how many pallets of bottled water are required for the drop?

45

20

18

75

Cevabı ve açıklamayı göster

Cevap: $45$

Cevap

The correct answer is

45

pallets of bottled water.

The correct answer is calculated by setting up a proportion based on the part-to-part ratio. The MREs represent

2

parts of the ratio, which equals

30

pallets. Therefore, one part equals

15

pallets. The water represents

3

parts, so

3 \times 15 = 45

pallets of water.

Adım Adım Çözüm

1

Identify the given ratio and known quantity.

The ratio of MREs to water is

2:3

, and there are

30

pallets of MREs.

Establishing the relationship between the parts is necessary to find the unknown quantity.

2

Determine the multiplier for the ratio.

30 \div 2 = 15

Since the

2

parts in the ratio represent

30

actual pallets, dividing determines the value of one part.

3

Calculate the unknown quantity using the multiplier.

3 \times 15 = 45

Multiplying the water ratio (

3

) by the value of one part (

15

) gives the actual number of water pallets.

Anahtar Kavram

Basic part-to-part ratio calculation involving finding a missing quantity when one part is known.

Soru 7Soru →

Match each quantity relationship to its equivalent simplified ratio.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The unsimplified ratios match to their reduced forms as follows: instructors to recruits (

10:50

) is

1:5

, trucks to vans (

12:8

) is

3:2

, fuel to oil (

15:5

) is

3:1

, and rifles to sidearms (

20:15

) is

4:3

.

Each relationship is found by writing down the initial numerical counts in the order specified and reducing them to their lowest integer terms using their greatest common factors.

Adım Adım Çözüm

1

Set up the initial part-to-part ratio for each scenario in the exact order requested by the text.

The raw ratios are

10:50

,

12:8

,

15:5

, and

20:15

.

Ratio order matters. Ensuring the first mentioned item is the first number in the ratio prevents inverted answers.

2

Simplify each ratio by finding the greatest common factor (GCF) for each pair and dividing both numbers by it.

10:50

reduces to

1:5

.

12:8

reduces to

3:2

.

15:5

reduces to

3:1

.

20:15

reduces to

4:3

.

A ratio is properly expressed when the two numbers have no common factors other than

1

.

Anahtar Kavram

Basic Ratios

Soru 8Soru →

A structural engineering team is mixing a specialized epoxy resin containing base, hardener, and silica filler in a strict ratio of $5:2:1$ by weight. If the team uses exactly $35$ pounds of the base component, what is the total weight, in pounds, of the prepared epoxy mixture?

Cevabı ve açıklamayı göster

Cevap: 56

Cevap

The total weight of the prepared epoxy mixture is 56 pounds.

The components are mixed in a ratio of

5:2:1

, which combines to make a total of

8

parts (

5 + 2 + 1 = 8

). We know the base component accounts for

5

of those parts and weighs

35

pounds. This means a single part weighs

7

pounds (

35 \div 5 = 7

). To find the total mixture weight, multiply the total number of parts (

8

) by the weight of a single part (

7

), resulting in

56

pounds.

Adım Adım Çözüm

1

Calculate the total number of parts in the given ratio.

5 + 2 + 1 = 8

total parts.

To establish the relationship between the individual components and the entire mixture.

2

Find the weight equivalent of one ratio part using the known base component.

35 \div 5 = 7

pounds per part.

The base component represents

5

parts of the ratio and weighs

35

pounds, so dividing its weight by its parts gives the unit multiplier.

3

Calculate the total weight of the mixture.

8 \times 7 = 56

pounds.

Multiplying the total number of ratio parts by the weight of a single part yields the overall total weight.

Anahtar Kavram

Solving part-to-whole ratio problems by finding the value of a single unit part.

Alternatif Yöntem

Calculate the individual weights of the missing components first. Hardener =

2 \times 7 = 14

pounds. Silica =

1 \times 7 = 7

pounds. Then, add these to the given base weight:

35 + 14 + 7 = 56

pounds.

Tahmini Süre:1m 0s

Soru 9Soru →

A civil engineering unit is mixing concrete for a rapid runway repair. The specialized mixture requires a weight ratio of $3$ parts Portland cement to $5$ parts aggregate. If a repair job requires a total of $400$ pounds of this dry mixture, how many pounds of Portland cement are needed?

50

150

240

250

Cevabı ve açıklamayı göster

Cevap: $150$

Cevap

The correct amount is

150

pounds.

The mixture consists of

3

parts cement and

5

parts aggregate, meaning there are

8

parts in total. Since the entire mixture weighs

400

pounds, each part weighs

50

pounds (

400 \div 8

). To find the amount of Portland cement, which represents

3

of those parts, we multiply

50

by

3

to get

150

pounds.

Adım Adım Çözüm

1

Determine the total number of parts in the given ratio.

3 \text{ (cement)} + 5 \text{ (aggregate)} = 8 \text{ total parts}

Because the

400

pounds represents the entire mixture, we need to know the total parts that make up that whole mixture.

2

Calculate the weight of one single part.

400 \div 8 = 50 \text{ pounds per part}

Dividing the total weight by the total number of parts gives the value of a single proportional unit.

3

Calculate the total weight of the Portland cement.

50 \times 3 = 150 \text{ pounds}

The ratio specifies

3

parts of Portland cement, so we multiply the weight of one part by

3

.

Anahtar Kavram

Solving part-to-whole ratio problems by finding the sum of the ratio parts and determining the unit value of a single part.

Soru 10Soru →

A naval maintenance crew is preparing an industrial cleaning solution for ship deck equipment. The standard procedure requires mixing chemical solvent and distilled water in a ratio of $3:2$ . If the crew needs to prepare a total of $150$ gallons of the cleaning solution, how many gallons of chemical solvent are required?

60

90

100

225

Cevabı ve açıklamayı göster

Cevap: $90$

Cevap

The required amount of chemical solvent is

90

gallons.

The correct answer accurately determines that the mixture consists of 5 total parts (3 parts solvent + 2 parts water). Dividing the total 150 gallons by 5 yields 30 gallons per part. Multiplying this by the 3 parts needed for the chemical solvent results in 90 gallons.

Adım Adım Çözüm

1

Determine the total number of parts in the ratio.

3 \text{ (solvent)} + 2 \text{ (water)} = 5 \text{ total parts}

To find the fractional share of the whole, you must first establish how many total proportional parts make up the complete mixture.

2

Calculate the volume of a single part by dividing the total volume by the total number of parts.

150 \text{ gallons} \div 5 \text{ parts} = 30 \text{ gallons per part}

This establishes the baseline unit value that can be scaled to find any individual component's volume.

3

Multiply the single part volume by the number of solvent parts required by the ratio.

30 \text{ gallons/part} \times 3 \text{ parts} = 90 \text{ gallons}

The ratio dictates there are 3 parts of solvent for every complete batch of the mixture.

Anahtar Kavram

Calculating a specific part from a total whole using a part-to-part ratio.

Tahmini Süre:1m 0s

Soru 11Soru →

A motor pool tracks the inventory of tactical vehicles and support vehicles assigned to different units. Match each unit's vehicle inventory to its equivalent simplified ratio of tactical vehicles to support vehicles.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Alpha matches to

3:1

, Bravo matches to

3:4

, Charlie matches to

7:3

, and Delta matches to

7:5

.

Each correct pairing is identified by writing the initial inventory as a part-to-part ratio in the specified order (tactical to support), then reducing the numbers by dividing both terms by their greatest common divisor.

Adım Adım Çözüm

1

Set up the initial ratio for Alpha Unit as tactical to support.

45:15

The question specifically asks for the ratio of tactical vehicles to support vehicles in that exact order.

2

Simplify the ratio for Alpha Unit by finding the greatest common divisor (GCD).

3:1

The GCD of

45

and

15

is

15

.

45 \div 15 = 3

and

15 \div 15 = 1

.

3

Set up and simplify the ratio for Bravo Unit (

24

to

32

).

3:4

The GCD of

24

and

32

is

8

.

24 \div 8 = 3

and

32 \div 8 = 4

.

4

Set up and simplify the ratio for Charlie Unit (

42

to

18

).

7:3

The GCD of

42

and

18

is

6

.

42 \div 6 = 7

and

18 \div 6 = 3

.

5

Set up and simplify the ratio for Delta Unit (

35

to

25

).

7:5

The GCD of

35

and

25

is

5

.

35 \div 5 = 7

and

25 \div 5 = 5

.

Anahtar Kavram

To find an equivalent simplified ratio, establish the correct part-to-part order and divide both quantities by their greatest common divisor.

Tahmini Süre:1m 30s

Soru 12Soru →

A medical logistics unit prepares field trauma kits. The weight ratio of bandages to antiseptic solution in each bulk shipment is strictly maintained at $3:4$ . If a particular shipment contains $12$ pounds of bandages, what is the required weight of the antiseptic solution in ounces?

16

256

64

144

Cevabı ve açıklamayı göster

Cevap: 256

Cevap

The correct weight of the antiseptic solution is 256 ounces.

The ratio of bandages to antiseptic is

3:4

. Since

12

pounds of bandages represents

3

parts of the ratio, each part is equal to

4

pounds (

12 \div 3 = 4

). The antiseptic represents

4

parts, so its weight is

4 \times 4 = 16

pounds. Finally, to find the weight in ounces, multiply by

16

(since there are

16

ounces in a standard pound), yielding

16 \times 16 = 256

ounces.

Adım Adım Çözüm

1

Set up a proportion using the given ratio of bandages to antiseptic (

3:4

).

\frac{3}{4} = \frac{12}{x}

The weight of the items must maintain the specific part-to-part ratio given in the problem.

2

Solve for

x

to find the weight of the antiseptic in pounds.

3x = 48 \Rightarrow x = 16

pounds

Cross-multiplying and dividing isolates the unknown quantity of antiseptic.

3

Convert the weight of the antiseptic from pounds to ounces.

16 \text{ pounds} \times 16 \text{ ounces/pound} = 256 \text{ ounces}

The question explicitly requests the final answer in ounces.

Anahtar Kavram

Solving basic ratios and applying unit conversions.

Soru 13Soru →

An aviation maintenance squadron stocks a specific fastener kit containing standard bolts, lock washers, and retaining nuts in a ratio of $7:4:3$ . If a master storage bin contains a total of $840$ of these combined items in this exact ratio, how many lock washers are in the bin?

Cevabı ve açıklamayı göster

Cevap: 240

Cevap

There are 240 lock washers in the bin.

The total number of items (

840

) is divided by the sum of all ratio parts (

14

) to find the value of a single share (

60

). This share is then multiplied by the specific ratio number corresponding to lock washers (

4

) to find the final quantity (

240

).

Adım Adım Çözüm

1

Calculate the total number of parts in the ratio.

7 + 4 + 3 = 14

parts

To determine what fraction of the total bin corresponds to a single proportional unit.

2

Determine the physical number of items represented by one part.

840 \div 14 = 60

items

Dividing the total inventory by the total ratio parts gives the baseline value of a single share.

3

Calculate the specific number of lock washers.

4 \times 60 = 240

lock washers

The ratio specifies there are

4

parts of lock washers, and each part equals

60

items.

Anahtar Kavram

Allocating a total known quantity into specific amounts based on a multi-term part-to-part ratio.

Tahmini Süre:1m 0s

Soru 14Soru →

An armored battalion maintains a strict ratio of combat crew members to maintenance personnel of $7:3$ . If there are $210$ combat crew members currently assigned to the battalion, how many maintenance personnel are assigned?

300

63

490

90

Cevabı ve açıklamayı göster

Cevap: $90$

Cevap

There are

90

maintenance personnel assigned to the battalion.

The ratio of combat crew to maintenance personnel is given as

7:3

. This means for every

7

combat crew members, there are

3

maintenance personnel. Since there are

210

combat crew members, we can set up the proportion:

7/3 = 210/M

. Solving for

M

, we get

7M = 630

, which means

M = 90

.

Adım Adım Çözüm

1

Set up a proportion using the given ratio of combat crew to maintenance personnel.

\frac{7}{3} = \frac{210}{M}

Proportions allow us to find a missing quantity when the ratio between two parts is known.

2

Solve the proportion for the number of maintenance personnel (

M

).

7 \times M = 210 \times 3 \Rightarrow 7M = 630 \Rightarrow M = 90

Cross-multiplying and then dividing by

7

isolates the variable

M

to provide the final answer.

Anahtar Kavram

Solving for a missing part in a two-term ratio

Tahmini Süre:1m 0s

Soru 15Soru →

A quartermaster is organizing deployment cargo for four different platoons. Match each platoon's cargo inventory to the corresponding simplified ratio of the first listed item to the second listed item.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Platoon Alpha matches to

3:1

, Platoon Bravo matches to

2:3

, Platoon Charlie matches to

3:5

, and Platoon Delta matches to

4:1

.

Each platoon's inventory forms a direct part-to-part ratio that can be simplified by dividing both quantities by their greatest common factor (GCF). Platoon Alpha's

45:15

reduces to

3:1

(GCF is

15

). Platoon Bravo's

24:36

reduces to

2:3

(GCF is

12

). Platoon Charlie's

60:100

reduces to

3:5

(GCF is

20

). Platoon Delta's

120:30

reduces to

4:1

(GCF is

30

).

Adım Adım Çözüm

1

Determine the simplified ratio for Platoon Alpha (

45

rations to

15

water).

The greatest common factor is

15

. Dividing both numbers by

15

yields

3:1

.

Simplifying the ratio reveals the baseline relationship between the two quantities.

2

Determine the simplified ratio for Platoon Bravo (

24

batteries to

36

flares).

The greatest common factor is

12

. Dividing both numbers by

12

yields

2:3

.

Both terms must be reduced completely to find the correct matching equivalent.

3

Determine the simplified ratio for Platoon Charlie (

60

sandbags to

100

stakes).

The greatest common factor is

20

. Dividing both numbers by

20

yields

3:5

.

Identifying the highest common divisor ensures the ratio is in its simplest form.

4

Determine the simplified ratio for Platoon Delta (

120

standard rounds to

30

tracer rounds).

The greatest common factor is

30

. Dividing both numbers by

30

yields

4:1

.

Applying the same simplification principle resolves the final pairing.

Anahtar Kavram

Simplifying basic part-to-part ratios by identifying and dividing by the greatest common factor.

Tahmini Süre:1m 30s

Soru 16Soru →

A military installation allocates its annual training budget between field exercises and classroom instruction in a ratio of $5:2$ . If the total annual training budget is $\$84,000$ , how much money is allocated to classroom instruction per month?

\$2,800

\$2,000

\$24,000

\$5,000

Cevabı ve açıklamayı göster

Cevap: $\$2,000$

Cevap

The correct answer is

\$2,000

.

The total budget is divided into

7

equal parts (

5 + 2

). Since classroom instruction receives

2

parts, its annual allocation is

\frac{2}{7}

of

\$84,000

, which is

\$24,000

. Dividing this annual amount by

12

months gives a monthly allocation of

\$2,000

.

Adım Adım Çözüm

1

Determine the total number of parts in the ratio.

5 + 2 = 7

total parts.

To find the value of a single share of the budget, the total amount must be divided by the total number of parts.

2

Calculate the value of one part of the budget.

\$84,000 \div 7 = \$12,000

per part.

This establishes the base unit for the ratio.

3

Determine the annual budget for classroom instruction.

2 \times \$12,000 = \$24,000

.

Classroom instruction corresponds to

2

parts of the

5:2

ratio.

4

Convert the annual budget to a monthly budget.

\$24,000 \div 12 = \$2,000

.

The question specifically asks for the monthly allocation.

Anahtar Kavram

Calculating proportional shares of a total amount and converting between time periods.

Tahmini Süre:1m 0s

Soru 17Soru →

A cybersecurity task force is composed of junior analysts and senior specialists in a ratio of $7:2$ . If the task force has a total of $126$ members, how many senior specialists are on the team?

28

36

98

14

Cevabı ve açıklamayı göster

Cevap: $28$

Cevap

There are

28

senior specialists on the team.

The correct answer is found by first adding the components of the ratio (

7 + 2 = 9

) to represent the entire task force. Next, divide the total number of members (

126

) by

9

to determine that each ratio 'part' equals

14

members. Finally, multiply this unit value by the

2

parts that represent the senior specialists (

14 \times 2 = 28

).

Adım Adım Çözüm

1

Determine the total number of parts in the given ratio.

7 + 2 = 9

total parts.

To find the value of a single part relative to the entire group, you must first know how many equal parts make up the whole.

2

Calculate the numerical value of one single part.

126 \div 9 = 14

members per part.

Dividing the total number of members by the total ratio parts gives the quantity represented by one unit.

3

Multiply the value of one part by the number of parts designated for senior specialists.

14 \times 2 = 28

senior specialists.

The ratio states there are

2

parts of senior specialists for every

7

parts of junior analysts.

Anahtar Kavram

Calculating a specific part from a total quantity using a part-to-part ratio.

Soru 18Soru →

A forward operating base maintains a stockpile of ammunition, food, and medical supplies in a weight ratio of 5:3:2. An incoming supply convoy delivers an additional 3 tons of food and 8 tons of medical supplies, while the ammunition stockpile remains unchanged. After the delivery, the new weight ratio of food to medical supplies becomes 4:3. What was the total weight of the entire stockpile before the convoy arrived?

20 tons

23 tons

115 tons

230 tons

Cevabı ve açıklamayı göster

Cevap: 230 tons

Cevap

The total weight of the entire stockpile before the convoy arrived was 230 tons.

The original weights can be expressed proportionally as

5x

(ammunition),

3x

(food), and

2x

(medical supplies), totaling

10x

. After adding the newly delivered amounts, the new weights for food and medical supplies become

3x + 3

and

2x + 8

. Setting their ratio equal to 4:3 yields the equation

\frac{3x + 3}{2x + 8} = \frac{4}{3}

. Cross-multiplying gives

9x + 9 = 8x + 32

, which simplifies to

x = 23

. The total original weight is therefore

10x = 10(23) = 230

tons.

Adım Adım Çözüm

1

Define the original weights of the supplies using a common multiplier

x

.

Ammunition =

5x

, Food =

3x

, Medical =

2x

. Total original weight =

5x + 3x + 2x = 10x

.

A ratio represents proportional parts of a whole. Multiplying each ratio term by a constant

x

gives expressions for their actual quantities.

2

Set up an algebraic expression for the new weights of food and medical supplies after the delivery.

New Food =

3x + 3

; New Medical =

2x + 8

.

The convoy delivered 3 tons of food and 8 tons of medical supplies, which are added to their respective original expressions.

3

Create a proportion using the new ratio of food to medical supplies provided in the problem.

\frac{3x + 3}{2x + 8} = \frac{4}{3}

The problem states that after the delivery, the ratio of food to medical supplies becomes 4:3.

4

Solve the proportion for

x

using cross-multiplication.

3(3x + 3) = 4(2x + 8) \Rightarrow 9x + 9 = 8x + 32 \Rightarrow x = 23

.

Cross-multiplying eliminates the fractions, creating a linear equation that can be solved for the common multiplier

x

.

5

Calculate the total original weight of the stockpile by substituting the value of

x

.

10(23) = 230

tons.

The question asks for the total weight of the entire stockpile before the delivery, which is represented by the expression

10x

.

Anahtar Kavram

Setting up and solving algebraic proportions from multi-term ratios after quantities undergo additive changes.

Tahmini Süre:1m 30s

Soru 19Soru →

An engine transmission system uses three interconnected gears: Gear A, Gear B, and Gear C. The ratio of the number of teeth on Gear A to the number of teeth on Gear B is $4:3$ . The ratio of the number of teeth on Gear B to the number of teeth on Gear C is $5:2$ . If Gear C has exactly $18$ teeth, what is the total number of teeth on all three gears combined?

Cevabı ve açıklamayı göster

Cevap: 123

Cevap

123

The correct answer is found by linking the two separate proportions using their common element, Gear B. By converting the A:B ratio (

4:3

) and the B:C ratio (

5:2

) to share a common value for B (

15

), we get a unified, continuous ratio for A:B:C of

20:15:6

. The problem states that Gear C has

18

teeth. Since Gear C represents

6

parts in our combined ratio, each part must equal

3

teeth (

18 \div 6 = 3

). The total number of parts across all three gears is

41

(

20 + 15 + 6

). Multiplying the

41

total parts by

3

teeth per part results in a total of

123

teeth for the entire system.

Adım Adım Çözüm

1

Align the separate ratios based on the common element.

Gear A : Gear B =

4:3

and Gear B : Gear C =

5:2

.

To compare all three gears simultaneously, Gear B must have the same value in both ratios.

2

Find a common multiple for the ratio numbers representing Gear B (

3

and

5

).

The least common multiple of

3

and

5

is

15

.

Creating a common denominator allows us to link the two independent proportions.

3

Scale both ratios so Gear B is represented by

15

parts.

Ratio A:B becomes

(4 \times 5):(3 \times 5) = 20:15

. Ratio B:C becomes

(5 \times 3):(2 \times 3) = 15:6

.

Multiplying both sides of a ratio by the same number maintains the proportion.

4

Combine into a single three-part ratio and determine total parts.

Combined ratio A:B:C is

20:15:6

. Total ratio parts =

20 + 15 + 6 = 41

.

This single ratio precisely maps the relationships between all three gears in the system.

5

Calculate the multiplier using Gear C's known teeth count.

6

parts =

18

teeth. Therefore,

1

part =

18 / 6 = 3

teeth.

This establishes the real-world value of a single ratio unit in this specific transmission system.

6

Calculate the total number of teeth on all gears combined.

41

total parts

\times 3

teeth per part =

123

teeth.

Multiplying the total number of parts by the value of a single part gives the final aggregate quantity.

Anahtar Kavram

Combining overlapping ratios by calculating the least common multiple of the shared term, then scaling the combined ratio to determine unknown totals.

Soru 20Soru →

Match each military and logistics operational scenario to the correct final mathematical ratio. Read the conditions carefully, as some require calculating a new ratio after a change occurs.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct matches are: Scenario 1 maps to 5:14, Scenario 2 maps to 2:7, Scenario 3 maps to 15:16, and Scenario 4 maps to 9:25.

Each scenario involves distinct ratio logic: Scenario 1 requires combining parts to find a whole. Scenarios 2 and 4 require breaking a total into parts using an initial ratio, subtracting from one part, and writing a new simplified ratio. Scenario 3 requires using part-to-part logic to find an unknown part given a specific base, then comparing the two results.

Adım Adım Çözüm

1

Calculate the ratios for the Naval Strike Group (Scenario 1).

The total proportion is

2

(cruisers) +

5

(destroyers) +

7

(frigates) =

14

. The ratio of destroyers to total ships is

5:14

.

You must establish the total baseline by summing the parts before finding the part-to-whole ratio.

2

Determine the new personnel ratio (Scenario 2).

Initially, officers =

18

and enlisted =

42

. Subtracting

6

officers leaves

12

. The new ratio is

12:42

, simplified to

2:7

.

Changes to one subset of a population require determining the original absolute values first.

3

Compare the fuel additive amounts (Scenario 3).

Correct additive is

\frac{3}{8} \times 40 = 15

. Mistaken additive is

\frac{4}{10} \times 40 = 16

. The ratio is

15:16

.

Scaling both ratios up to the common base fuel amount of

40

reveals the exact additive quantities to compare.

4

Adjust the convoy vehicles ratio (Scenario 4).

Initially, cargo =

25

and escort =

10

. Subtracting

1

escort leaves

9

. The required ratio of escort to cargo is

9:25

.

Calculating initial absolute quantities is necessary before applying the subtraction of

1

vehicle and interpreting the final specific order requested.

Anahtar Kavram

Applying part-to-part and part-to-whole ratio relationships to calculate absolute values, applying condition changes, and then re-evaluating and simplifying the final ratios.

Alternatif Yöntem

For Scenario 2, you can also calculate the fractional drop without finding absolute enlisted numbers. The officer count drops from

18

to

12

, which is exactly

\frac{2}{3}

of the original amount. Thus, the new ratio must simply be

\frac{2}{3}

of the original officer portion (

3

) against the same enlisted portion (

7

), resulting directly in a

2:7

ratio.

Tahmini Süre:2m 30s

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