Ratios and Proportions Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 2

Soru 21Soru →

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 22Soru →

A submarine leaves port with enough provisions to feed its standard crew of $120$ personnel for $60$ days. Before departure, $30$ additional mission specialists are assigned to the submarine. If the daily ration per person remains constant, how many days will the provisions last the newly expanded crew?

Cevabı ve açıklamayı göster

Cevap: 48

Cevap

48

Because the total amount of food remains constant, an increase in personnel causes a proportional decrease in the number of days the food will last. The product of personnel and days is constant:

120 \times 60 = 150 \times x

. Solving for

x

gives

7200 / 150 = 48

days.

Adım Adım Çözüm

1

Calculate the total amount of provisions available.

120 \text{ personnel} \times 60 \text{ days} = 7200 \text{ person-days}

In an inverse proportion involving resources, the product of the number of consumers and the time the resource lasts represents the constant total resource.

2

Calculate the total number of personnel after the addition.

120 + 30 = 150 \text{ personnel}

The problem states that 30 additional specialists were assigned, so the new crew size is the sum of the original and additional personnel.

3

Calculate the new duration the provisions will last.

7200 \text{ person-days} \div 150 \text{ personnel} = 48 \text{ days}

Dividing the total constant resource by the new number of consumers yields the new time duration.

Anahtar Kavram

Inverse Proportions

Tahmini Süre:1m 0s

Soru 23Soru →

A motor pool technician is mixing a cleaning solvent and water in a ratio of $2:5$ to fill a $35$ -gallon container. How many gallons of cleaning solvent are needed?

7

10

14

25

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10 gallons

The total number of ratio parts is

2 + 5 = 7

. The total volume is

35

gallons, so each part represents

35 \div 7 = 5

gallons. Since the cleaning solvent corresponds to

2

parts, the amount of solvent needed is

2 \times 5 = 10

gallons.

Adım Adım Çözüm

1

Find the total number of parts in the ratio.

2 + 5 = 7

total parts

The ratio

2:5

means the total mixture is made up of

7

equal parts.

2

Calculate the volume of a single part.

35 \div 7 = 5

gallons per part

Dividing the total volume by the total number of parts gives the amount for one individual part.

3

Calculate the volume of the cleaning solvent.

2 \times 5 = 10

gallons

The cleaning solvent represents

2

parts of the total mixture.

Anahtar Kavram

Dividing a total quantity into proportional parts based on a given part-to-part ratio.

Soru 24Soru →

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 25Soru →

A supply sergeant initially distributes $2,400$ rounds of specialized training ammunition among three firing squads—Alpha, Bravo, and Charlie—in a ratio of $2:3:5$ , respectively. During the drill, Squad Bravo requests and is issued exactly $180$ additional rounds.

To maintain the exact original $2:3:5$ distribution ratio among the three squads, the sergeant must also issue additional rounds to Alpha and Charlie. How many total additional rounds must be issued to Squads Alpha and Charlie combined to perfectly restore the original ratio?

Cevabı ve açıklamayı göster

Cevap: 420

Cevap

420

By determining that Bravo's 180 additional rounds correspond to its 3 parts in the ratio, we can establish that the proportional increase per part is 60 rounds (180 ÷ 3). Since Alpha and Charlie make up 7 parts combined (2 + 5), they require an additional 7 × 60 = 420 rounds to maintain the ratio.

Adım Adım Çözüm

1

Calculate the initial number of rounds representing a single ratio part.

240 rounds per part.

The total of 2,400 rounds is distributed across 2 + 3 + 5 = 10 total parts.

2

Determine Squad Bravo's new total amount of ammunition.

900 rounds.

Bravo initially had 3 parts (3 × 240 = 720). Adding the 180 new rounds brings their total to 720 + 180 = 900 rounds.

3

Calculate the new value of a single ratio part required to maintain the 2:3:5 distribution.

300 rounds per part.

Bravo's new total of 900 rounds must represent its 3 parts in the ratio. Therefore, 900 ÷ 3 = 300.

4

Calculate the total additional rounds needed for Alpha and Charlie combined.

420 rounds.

The proportional increase per ratio part is 300 - 240 = 60 rounds. Alpha and Charlie represent 2 + 5 = 7 parts combined. 7 parts × 60 rounds = 420 rounds.

Anahtar Kavram

Dividing quantities based on a given ratio and recalculating proportional parts after a specific adjustment.

Alternatif Yöntem

Instead of calculating the initial and final totals for each squad, analyze the proportional change directly. Squad Bravo's allocation increases by 180 rounds. Since Bravo represents 3 parts of the ratio, the increase is 180 ÷ 3 = 60 rounds per ratio part. Squads Alpha and Charlie account for 2 + 5 = 7 ratio parts combined. Therefore, their combined additional requirement is simply 7 parts × 60 rounds/part = 420 rounds.

Tahmini Süre:2m 30s

Soru 26Soru →

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 27Soru →

A mess hall cook prepares a large batch of stew. The recipe requires a total of $60$ pounds of meat and potatoes. If the ratio of meat to potatoes is $3:2$ , how many pounds of meat are needed?

12

20

24

36

Cevabı ve açıklamayı göster

Cevap: $36$

Cevap

36

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

3 + 2 = 5

). Next, divide the total weight (

60

pounds) by

5

to find the weight of a single part (

12

pounds). Finally, multiply this unit weight by the number of parts designated for meat (

3 \times 12 = 36

pounds).

Adım Adım Çözüm

1

Find the total number of parts in the ratio.

3 + 2 = 5

total parts.

To distribute the total weight correctly, we first need to determine how many proportional parts make up the whole.

2

Determine the weight of a single part.

60 \div 5 = 12

pounds per part.

Dividing the total weight by the total number of parts gives the value of one unit in the ratio.

3

Calculate the total weight of the meat.

3 \times 12 = 36

pounds.

The ratio states there are

3

parts of meat. Multiplying the weight of one part by

3

gives the final amount of meat needed.

Anahtar Kavram

Dividing a total quantity into parts based on a given ratio.

Tahmini Süre:45s

Soru 28Soru →

A quartermaster purchases $2$ dozen identical tactical flashlights for a total cost of $\$720$ . What is the unit price of a single flashlight?

\$3

\$30

\$60

\$360

Cevabı ve açıklamayı göster

Cevap: $\$30$

Cevap

The correct unit price is

\$30

per flashlight.

To find the unit price, the total cost must be divided by the total number of individual items. First, convert

2

dozen into a specific quantity by multiplying by

12

, yielding

24

flashlights. Then, divide the total cost of

\$720

by

24

, which equals

\$30

per flashlight.

Adım Adım Çözüm

1

Determine the total number of flashlights purchased.

2 \text{ dozen} = 2 \times 12 = 24 \text{ flashlights}

You must know the exact number of individual items before you can calculate the cost of a single item.

2

Divide the total cost by the total number of items to find the unit price.

\$720 \div 24 = \$30

Unit price is found by dividing the total amount spent by the total quantity received.

Anahtar Kavram

Unit Price Calculation

Tahmini Süre:45s

Soru 29Soru →

A logistics officer needs to distribute $150$ tactical backpacks between two infantry squads in a ratio of $2:3$ . How many backpacks will the squad with the smaller share receive?

Cevabı ve açıklamayı göster

Cevap: 60

Cevap

60

To solve the problem, we first determine that the total ratio consists of

5

parts (

2 + 3

). Dividing the

150

total backpacks by

5

parts gives us

30

backpacks for every single part. Because the question asks for the squad with the smaller share, we multiply the

30

backpacks by the smaller ratio number (

2

), which results in

60

backpacks.

Adım Adım Çözüm

1

Calculate the total number of parts in the ratio by adding the given values.

2 + 3 = 5

total parts.

This establishes the total number of equal shares the backpacks will be divided into.

2

Determine the number of backpacks in a single part by dividing the total amount by the total parts.

150 \div 5 = 30

backpacks per part.

Finding the unit value allows us to calculate any specific share in the proportion.

3

Calculate the smaller share by multiplying the unit value by the smaller number in the ratio.

30 \times 2 = 60

backpacks.

The question asks for the smaller share, which corresponds to the

2

parts in the

2:3

ratio.

Anahtar Kavram

Dividing a total quantity into a given ratio

Soru 30Soru →

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 31Soru →

Match each inverse proportion scenario to its correct calculated value.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Each scenario represents an inverse proportion and must be matched with the value that maintains the constant product of the initial conditions.

Each match is mathematically determined by setting up an inverse proportion equation where the product of the initial states equals the product of the final states (

x_1 \cdot y_1 = x_2 \cdot y_2

). Dividing the initial product by the new given value provides the correct corresponding answer.

Adım Adım Çözüm

1

Identify that each scenario represents an inverse relationship.

As one quantity increases (troops, speed, workers, gear teeth), the other quantity must decrease.

This determines that the product of the variables is constant (

x_1 \cdot y_1 = x_2 \cdot y_2

), rather than the ratio.

2

Calculate the constant product (

k

) for the initial conditions in each scenario.

The constants are

15,000

troop-days,

2,400\text{ miles}

,

96\text{ man-hours}

, and

7,200\text{ teeth-RPM}

.

The constant represents the total amount of work, distance, resources, or mechanical transfer that must remain unchanged.

3

Divide the constant product by the new given variable to find the unknown required value.

The resulting values are

20\text{ days}

,

4\text{ hours}

,

6\text{ hours}

, and

160\text{ RPM}

.

Solving the equation

x_1 \cdot y_1 = x_2 \cdot y_2

for the unknown variable

y_2

requires dividing the constant by

x_2

.

Anahtar Kavram

Inverse Proportions

Soru 32Soru →

A naval supply ship pumps $3,600$ gallons of fresh water into a destroyer's holding tanks over the course of $4$ hours. At what constant rate, in gallons per hour, is the water being pumped?

Cevabı ve açıklamayı göster

Cevap: 900

Cevap

900

To find the rate in gallons per hour, the total number of gallons (

3,600

) is divided by the total number of hours (

4

), resulting in

900

gallons per hour.

Adım Adım Çözüm

1

Identify the total quantity and the total time given in the scenario.

Total quantity =

3,600

gallons. Total time =

4

hours.

A unit rate requires knowing both the total amount and the corresponding time frame.

2

Divide the total gallons by the total hours to find the unit rate.

3,600 \div 4 = 900

Dividing the total amount by the number of hours yields the amount per single hour.

Anahtar Kavram

Calculating a basic unit rate by dividing a total quantity by a total time.

Soru 33Soru →

During a base renovation, a carpenter cuts a $5$ -foot wooden board into two pieces. If the lengths of the two pieces are in a ratio of $2:3$ , what is the length of the shorter piece in inches?

24

36

40

2

Cevabı ve açıklamayı göster

Cevap: $24$

Cevap

The shorter piece is

24

inches long.

First, convert the

5

-foot board to inches by multiplying by

12

, which gives

60

inches. The ratio

2:3

means there are

2 + 3 = 5

total equal parts. Dividing the

60

-inch board by

5

gives

12

inches per part. The shorter piece is

2

parts, so

2 \times 12 = 24

inches.

Adım Adım Çözüm

1

Convert the total length of the board from feet to inches.

5 \times 12 = 60

inches.

The question asks for the final answer in inches, so it is easiest to work in inches from the start.

2

Find the total number of parts in the ratio.

2 + 3 = 5

total parts.

A ratio of

2:3

means the whole board is divided into

5

equal segments.

3

Determine the length of one single part.

60 \div 5 = 12

inches per part.

Dividing the total length by the total number of parts gives the value of one part.

4

Calculate the length of the shorter piece.

12 \times 2 = 24

inches.

The shorter piece represents

2

parts of the ratio.

Anahtar Kavram

To divide a quantity in a given ratio, find the total number of parts by adding the ratio terms, divide the total quantity by this number to find the value of one part, and multiply by the relevant ratio term. Always ensure units are consistent.

Soru 34Soru →

A military detail fills $300$ sandbags in $150$ minutes. What is the constant rate at which the detail fills the sandbags, in sandbags per hour?

120

2

12

0.5

Cevabı ve açıklamayı göster

Cevap: 120

Cevap

120

The unit rate is found by first converting the time into hours (

150

minutes is

2.5

hours) and then dividing the total quantity (

300

sandbags) by this time, resulting in

120

sandbags per hour.

Adım Adım Çözüm

1

Convert the total time from minutes to hours.

150 \text{ minutes} \div 60 \text{ minutes/hour} = 2.5 \text{ hours}

The requested unit rate is in sandbags per hour, so the time must be expressed in hours.

2

Calculate the unit rate by dividing the total number of sandbags by the total time in hours.

300 \text{ sandbags} \div 2.5 \text{ hours} = 120 \text{ sandbags per hour}

A unit rate represents the quantity produced per single unit of time.

Anahtar Kavram

Calculating unit rates with time conversion

Soru 35Soru →

A naval shipyard assigns $15$ automated painting drones to coat the hull of a cruiser in exactly $2\text{ hours}$ . If $5$ of these drones are taken offline for maintenance before the job begins, how many minutes will it take the remaining drones to complete the coating?

80

360

180

3

Cevabı ve açıklamayı göster

Cevap: $180$

Cevap

It will take 180 minutes for the remaining drones to complete the hull coating.

The correct answer is

180

. First, subtract the

5

offline drones from the initial

15

to find that

10

drones are actively working. Because the number of drones and the time required are inversely proportional, their product remains constant. The equation is

15 \times 2 = 10 \times T_2

, which solves to

T_2 = 3\text{ hours}

. Finally, converting

3\text{ hours}

to minutes yields

3 \times 60 = 180\text{ minutes}

.

Adım Adım Çözüm

1

Determine the number of active drones.

15 - 5 = 10\text{ drones}

The 5 offline drones cannot work, so only the remaining drones will paint the hull.

2

Set up an inverse proportion equation.

15\text{ drones} \times 2\text{ hours} = 10\text{ drones} \times T_2

Work rate problems involve inverse proportions; as the number of workers decreases, the time required increases proportionally to keep the total work constant.

3

Solve for the new time (

T_2

) in hours.

30 = 10 \times T_2 \Rightarrow T_2 = 3\text{ hours}

Dividing the total required drone-hours (

30

) by the number of active drones (

10

) isolates the time.

4

Convert the required time into minutes.

3 \times 60 = 180\text{ minutes}

The question explicitly asks for the final answer in minutes, not hours.

Anahtar Kavram

Inverse Proportions

Soru 36Soru →

Match each military vehicle's travel scenario to its correct average unit rate in miles per hour.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The jeep matches to 40 mph, the helicopter to 150 mph, the truck to 55 mph, and the patrol boat to 36 mph.

Each unit rate is found by applying the formula for speed: Speed = Distance ÷ Time. Calculating this for each vehicle yields the correct matching pairs.

Adım Adım Çözüm

1

Calculate the unit rate for the jeep.

120 / 3 = 40 miles per hour

To find the average speed, divide total distance by total time.

2

Calculate the unit rate for the helicopter.

300 / 2 = 150 miles per hour

To find the average speed, divide total distance by total time.

3

Calculate the unit rate for the supply truck.

220 / 4 = 55 miles per hour

To find the average speed, divide total distance by total time.

4

Calculate the unit rate for the patrol boat.

180 / 5 = 36 miles per hour

To find the average speed, divide total distance by total time.

Anahtar Kavram

A unit rate compares a quantity to one unit of another quantity, often calculated by dividing the total amount by the total time or number of items.

Soru 37Soru →

A reconnaissance drone squadron currently takes $14\text{ hours}$ to completely map a designated tactical sector when using $6$ identical drones simultaneously. If the task force commander requires the exact same sector to be mapped in $4\text{ hours}$ , how many total drones must be deployed?

Cevabı ve açıklamayı göster

Cevap: 21

Cevap

21

drones

The scenario describes an inverse proportion because increasing the number of active drones decreases the time required to finish the mapping. The total mapping workload is a constant

84

drone-hours (

6\text{ drones} \times 14\text{ hours}

). To complete this exact same workload in a compressed timeframe of

4

hours, a total of

21

drones are needed (

84 \div 4

).

Adım Adım Çözüm

1

Identify the relationship between the variables.

The number of drones and the time required are inversely proportional.

Completing a fixed amount of work faster requires proportionally more equipment.

2

Calculate the total amount of work required (the constant of variation).

6\text{ drones} \times 14\text{ hours} = 84\text{ drone-hours}

In an inverse proportion (

x \times y = k

), the product of the two variables remains constant.

3

Calculate the new number of drones required for the target time.

84\text{ drone-hours} \div 4\text{ hours} = 21\text{ drones}

Divide the total work constant by the new required time to solve for the missing variable.

Anahtar Kavram

Inverse proportions occur when one variable increases while another decreases such that their product remains constant (

x_1 \times y_1 = x_2 \times y_2

).

Soru 38Soru →

A landscape architect is preparing a design layout for a new rectangular community garden. On the layout, the garden measures $2.5\text{ inches}$ in width and $5\text{ inches}$ in length. The drawing uses a scale where $\frac{1}{4}\text{ inch}$ represents $3\text{ feet}$ . What is the actual area of the community garden in square feet?

112.5

150

180

1,800

Cevabı ve açıklamayı göster

Cevap: $1,800$

Cevap

The actual area of the community garden is

1,800

square feet.

The correct answer is found by first establishing how many feet each inch on the layout represents. Since a quarter of an inch represents 3 feet, one full inch represents 12 feet (4 times 3). Multiplying the layout dimensions by 12 provides the actual dimensions: a width of 30 feet and a length of 60 feet. Finally, multiplying the actual width by the actual length (30 x 60) gives the true area of 1,800 square feet.

Adım Adım Çözüm

1

Determine the unit scale factor for 1 inch.

Since

1/4\text{ inch} = 3\text{ feet}

, multiplying both sides by 4 gives

1\text{ inch} = 12\text{ feet}

.

Converting the scale to a 'per inch' rate makes it easier to apply to the drawing measurements.

2

Calculate the actual width and length of the garden.

Actual width =

2.5 \times 12 = 30\text{ feet}

. Actual length =

5 \times 12 = 60\text{ feet}

.

Applying the linear scale factor converts the map dimensions directly into real-world dimensions.

3

Calculate the area of the actual garden.

Area =

30\text{ feet} \times 60\text{ feet} = 1,800\text{ square feet}

.

The area of a rectangle is found by multiplying its length by its width.

Anahtar Kavram

Scale Drawings and Area Calculation

Soru 39Soru →

A civilian contractor works $5$ days a week for $8$ hours each day on a military base. If the contractor earns $\$840$ for the entire week, what is the contractor's hourly wage?

\$21

\$105

\$168

\$210

Cevabı ve açıklamayı göster

Cevap: \$21

Cevap

The contractor's hourly wage is

\$21

.

The total number of hours worked in the week is found by multiplying the

5

days by

8

hours per day, which equals

40

hours. The hourly wage is then calculated by dividing the total weekly earnings by the total hours worked:

\$840 \div 40 = \$21

per hour.

Adım Adım Çözüm

1

Calculate the total number of hours the contractor works in the week.

5 \text{ days} \times 8 \text{ hours/day} = 40 \text{ hours}

To find the hourly wage, the total earnings must be divided by the total hours worked.

2

Divide the total weekly earnings by the total hours worked to find the hourly wage.

\$840 \div 40 \text{ hours} = \$21 \text{ per hour}

The unit rate (hourly wage) is the ratio of total pay to total time.

Anahtar Kavram

Calculating a unit rate by determining the total quantity (hours) and dividing the total amount (earnings) by that quantity.

Soru 40Soru →

A hobbyist is building a scale model of a historic steam locomotive using a scale of $1:48$ . If the actual locomotive is $60\text{ feet}$ long, what is the length of the model locomotive in inches?

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Cevap: 15

Cevap

15

To find the length of the scale model, the actual length of the locomotive must first be converted into inches. Since there are

12\text{ inches}

in a foot,

60\text{ feet}

is equal to

720\text{ inches}

. Using the scale ratio of

1:48

, divide the actual length in inches by

48

to find the model's length. Calculating

720 \div 48

yields a model length of

15\text{ inches}

.

Adım Adım Çözüm

1

Convert the actual length of the locomotive from feet to inches.

60 \times 12 = 720\text{ inches}

The question asks for the model length in inches, so it is necessary to match the units before applying the scale factor.

2

Calculate the model length using the

1:48

scale ratio.

720 \div 48 = 15\text{ inches}

The scale

1:48

means the model is

48

times smaller than the actual object.

Anahtar Kavram

Applying scale ratios across different units of measurement.

Ratios and Proportions

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