Ratios and Proportions Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 3

Question 41Question →

A warehouse forklift moves $84$ cargo pallets in $6$ hours. At this constant rate, how many pallets does the forklift move per hour?

Show answer & explanation

Answer: 14

Answer

The forklift moves

14

pallets per hour.

To determine the unit rate, divide the total quantity (

84

pallets) by the total elapsed time (

6

hours). The result is a constant rate of

14

pallets per hour.

Step-by-Step Solution

1

Identify the total quantity of items and the total time.

Total pallets =

84

, Total time =

6

hours.

These are the two values needed to set up the unit rate calculation.

2

Divide the total pallets by the total hours.

84 \div 6 = 14

The unit rate 'pallets per hour' requires dividing the number of pallets by the number of hours.

Key Concept

Calculating unit rates

Estimated Time:45s

Question 42Question →

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

Show answer & explanation

Answer: $150$

Answer

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.

Step-by-Step Solution

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

.

Key Concept

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

Question 43Question →

A mess hall crew prepares $240$ field rations in $120$ minutes. What is the crew's constant preparation rate in rations per hour?

2

12

120

480

Show answer & explanation

Answer: 120

Answer

120

The rate is found by first converting

120

minutes into

2

hours, then dividing the

240

rations by

2

hours to obtain

120

rations per hour.

Step-by-Step Solution

1

Convert the given time from minutes to hours.

120 \text{ minutes} = 2 \text{ hours}

The question asks for the rate in rations per hour, so the time unit must be in hours.

2

Divide the total number of rations by the total time in hours.

240 \div 2 = 120

Dividing the total quantity by the total time calculates the unit rate.

Key Concept

Calculating a unit rate often requires first converting time into the requested units before performing division.

Question 44Question →

A contractor is analyzing a zoning plan for a commercial parking lot. The plan's legend indicates a scale of $1\text{ inch} = 10\text{ yards}$ . If the parking lot covers an area of $4\text{ square inches}$ on the zoning plan, what is the actual area of the parking lot in square feet?

120

400

1,200

3,600

Show answer & explanation

Answer: $3,600$

Answer

The actual area of the parking lot is

3,600

square feet.

The correct answer is found by first aligning the units: the scale of

1\text{ inch} = 10\text{ yards}

is equivalent to

1\text{ inch} = 30\text{ feet}

. Because we are dealing with area (a two-dimensional measurement), this linear scale must be squared, meaning

1\text{ square inch}

on the drawing represents

900\text{ square feet}

in reality (

30^2 = 900

). Finally, multiplying the drawing's area by this factor yields the actual area:

4 \times 900 = 3,600\text{ square feet}

.

Step-by-Step Solution

1

Convert the linear scale from yards to feet.

10\text{ yards} = 30\text{ feet}

, so the scale is

1\text{ inch} = 30\text{ feet}

.

The final question asks for the area in square feet, so it is easiest to align the units of the scale factor first.

2

Determine the area scale factor by squaring the linear scale.

1\text{ square inch} = (30\text{ feet}) \times (30\text{ feet}) = 900\text{ square feet}

.

Because area represents two dimensions, the linear scale must be squared to find out how much actual area one square inch on the drawing represents.

3

Multiply the drawing area by the area scale factor.

4\text{ square inches} \times 900\text{ square feet per square inch} = 3,600\text{ square feet}

.

This scales the blueprint measurement up to the actual real-world area.

Key Concept

When using a scale drawing to find a real-world area, the linear scale factor must be squared. Furthermore, all units must be carefully tracked and converted to match the requested final unit.

Question 45Question →

A logistics officer is reviewing purchase orders for safety equipment. Match each bulk purchase scenario to its correct unit price.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings are determined by dividing the total cost by the quantity for each scenario, yielding the unit rates of

5,

3,

6, and

4 respectively.

Each correct match is found by identifying the unit price using the formula: Total Cost ÷ Quantity.

Step-by-Step Solution

1

Calculate the unit price for the protective goggles.

60 / 12 =

5 per pair.

Unit price is total cost divided by quantity.

2

Calculate the unit price for the work gloves.

90 / 30 =

3 per pair.

Unit price is total cost divided by quantity.

3

Calculate the unit price for the heavy-duty flashlights.

48 / 8 =

6 per flashlight.

Unit price is total cost divided by quantity.

4

Calculate the unit price for the high-visibility vests.

100 / 25 =

4 per vest.

Unit price is total cost divided by quantity.

Key Concept

Calculating unit rates by dividing the total amount by the number of units.

Question 46Question →

An architect is designing a community center and reviewing the floor plan. The floor plan uses a scale of $\frac{3}{4}\text{ inch} = 5\text{ feet}$ . If the main hall measures $4.5\text{ inches}$ long on the floor plan, what is the actual length of the main hall in feet?

Show answer & explanation

Answer: 30

Answer

30

The correct answer is found by setting up a proportion or finding the unit rate. Since

\frac{3}{4}\text{ inch}

represents

5\text{ feet}

,

1\text{ inch}

represents

\frac{20}{3}\text{ feet}

. Multiplying the drawing measurement of

4.5\text{ inches}

by

\frac{20}{3}\text{ feet per inch}

yields exactly

30\text{ feet}

.

Step-by-Step Solution

1

Find the actual distance represented by one inch.

1\text{ inch} = 5 \div \frac{3}{4} = 5 \times \frac{4}{3} = \frac{20}{3}\text{ feet}

Establishing a unit rate simplifies calculating the actual length for any given map measurement.

2

Multiply the unit rate by the blueprint measurement.

4.5 \times \frac{20}{3} = \frac{9}{2} \times \frac{20}{3} = \frac{180}{6} = 30\text{ feet}

Multiplying the map length by the actual distance per inch gives the total actual length.

Key Concept

Solving scale drawing problems using proportions or unit rates.

Question 47Question →

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

Show answer & explanation

Answer: $90$

Answer

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.

Step-by-Step Solution

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.

Key Concept

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

Estimated Time:1m 0s

Question 48Question →

A maritime authority is reviewing a nautical chart to designate a restricted sailing zone. The chart uses a scale where $\frac{1}{2}\text{ inch}$ represents $30\text{ nautical miles}$ . If the restricted zone is drawn as a rectangle measuring $2\text{ inches}$ by $3\text{ inches}$ on the chart, what is the actual area of the restricted zone in square nautical miles?

360

1,350

21,600

2,160

Show answer & explanation

Answer: 21,600

Answer

21,600

The correct answer is found by first converting each chart dimension into its actual distance. Because a half inch represents 30 nautical miles, one full inch represents 60 nautical miles. Multiplying the chart's 2-inch and 3-inch dimensions by 60 yields actual dimensions of 120 and 180 nautical miles. Multiplying these true dimensions together gives a final area of 21,600 square nautical miles.

Step-by-Step Solution

1

Determine the linear scale for a full inch based on the provided fractional scale.

Since

1/2\text{ inch} = 30\text{ nautical miles}

, then

1\text{ inch} = 60\text{ nautical miles}

.

Establishing the unit rate for 1 inch simplifies the conversion of the chart dimensions.

2

Convert the chart dimensions to actual dimensions.

Width:

2\text{ inches} \times 60 = 120\text{ nautical miles}

. Length:

3\text{ inches} \times 60 = 180\text{ nautical miles}

.

Linear dimensions must be converted to actual lengths before computing the true area.

3

Calculate the actual area by multiplying the actual length and actual width.

120 \times 180 = 21,600\text{ square nautical miles}

.

The area of a rectangle is the product of its length and width.

Key Concept

Calculating true area from a scale drawing by converting linear dimensions first.

Question 49Question →

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.

Click a left item, then click its matching right item

Show answer & explanation

Answer

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.

Step-by-Step Solution

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

.

Key Concept

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

Estimated Time:1m 30s

Question 50Question →

A structural engineer is analyzing a blueprint for a steel bridge truss. The blueprint uses a scale where $\frac{7}{8}\text{ inch}$ represents an actual length of $21\text{ feet}$ . If a particular support beam measures $6.5\text{ inches}$ on the blueprint, what is the actual length of this beam in feet?

Show answer & explanation

Answer: 156

Answer

156

The correct answer is found by establishing a proportion based on the scale. Since

\frac{7}{8}\text{ inch}

equals

21\text{ feet}

,

1\text{ inch}

must equal

21 \div \frac{7}{8}

, which is

24\text{ feet}

. Multiplying the blueprint length of

6.5\text{ inches}

by this unit rate of

24

gives an actual length of

156\text{ feet}

.

Step-by-Step Solution

1

Determine the unit scale factor in feet per inch.

21 \div \frac{7}{8} = 24\text{ feet/inch}

Finding the actual distance represented by a single inch creates a simple multiplier for any dimension on the blueprint.

2

Multiply the measurement on the blueprint by the unit scale factor.

6.5 \times 24 = 156\text{ feet}

Scaling up the drawing measurement by the unit rate yields the actual real-world length of the beam.

Key Concept

Direct proportions and unit rates in scale drawings

Alternative Method

You can set up a direct proportion:

\frac{\frac{7}{8}}{21} = \frac{6.5}{x}

. Cross-multiplying gives

\frac{7}{8}x = 136.5

. Multiplying both sides by

\frac{8}{7}

yields

x = 156

.

Estimated Time:1m 0s

Question 51Question →

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

Show answer & explanation

Answer: 256

Answer

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.

Step-by-Step Solution

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.

Key Concept

Solving basic ratios and applying unit conversions.

Question 52Question →

A combat engineering detachment is mixing a specialized rapid-setting concrete. The dry mix requires sand, gravel, and cement in a ratio of $4:5:2$ by weight. If the engineers need to prepare exactly $3,300$ pounds of the dry mix for a runway repair, how many pounds of gravel are required?

Show answer & explanation

Answer: 1500

Answer

1500

To find the correct amount of gravel, the total weight of

3,300

pounds is divided by the total number of parts in the ratio (

4 + 5 + 2 = 11

) to find the weight of one part (

300

pounds). The gravel's share is 5 parts, so multiplying

300

pounds by 5 yields exactly

1,500

pounds.

Step-by-Step Solution

1

Find the total number of parts in the ratio.

4 + 5 + 2 = 11

total parts

To distribute the total weight proportionally, you first need to know how many equal parts make up the entire mixture.

2

Determine the weight of one single part.

3,300 \div 11 = 300

pounds

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

3

Calculate the specific weight required for the gravel.

300 \times 5 = 1,500

pounds

The ratio specifies 5 parts of gravel. Multiplying the weight of one part by 5 gives the total weight of the gravel.

Key Concept

Dividing a total quantity into given ratio parts.

Question 53Question →

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?

Show answer & explanation

Answer: 240

Answer

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

).

Step-by-Step Solution

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.

Key Concept

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

Estimated Time:1m 0s

Question 54Question →

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

Show answer & explanation

Answer: $90$

Answer

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

.

Step-by-Step Solution

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.

Key Concept

Solving for a missing part in a two-term ratio

Estimated Time:1m 0s

Question 55Question →

A refueling truck contains $150$ gallons of aviation fuel. The fuel is distributed among three training aircraft in a ratio of $2:3:5$ . How many quarts of fuel does the second aircraft receive? ( $1\text{ gallon} = 4\text{ quarts}$ )

360

45

180

300

Show answer & explanation

Answer: 180

Answer

180

The total number of ratio parts is

2 + 3 + 5 = 10

. Dividing the total

150

gallons by

10

parts gives

15

gallons per part. The second aircraft receives

3

parts, which is

3 \times 15 = 45

gallons. Converting to quarts,

45 \text{ gallons} \times 4 \text{ quarts/gallon} = 180 \text{ quarts}

.

Step-by-Step Solution

1

Calculate the total number of ratio parts.

2 + 3 + 5 = 10

parts

To find the value of a single part, we must divide the total amount by the sum of the ratio parts.

2

Determine the value of one part in gallons.

150 \div 10 = 15

gallons per part

This establishes the base unit for the ratio distribution.

3

Calculate the second aircraft's share in gallons.

3 \times 15 = 45

gallons

The second aircraft corresponds to the middle term in the

2:3:5

ratio, which is

3

parts.

4

Convert the share from gallons to quarts.

45 \times 4 = 180

quarts

The question specifically asks for the final answer in quarts.

Key Concept

Dividing in a Ratio with Unit Conversions

Question 56Question →

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.

Click a left item, then click its matching right item

Show answer & explanation

Answer

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

).

Step-by-Step Solution

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.

Key Concept

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

Estimated Time:1m 30s

Question 57Question →

Read the scenario and fill in the missing values based on the given ratio.

Fill in the blanks below

A medical supply depot is distributing

2,400

trauma kits among three field hospitals—Alpha, Bravo, and Charlie—in a ratio of

3:4:5

, respectively. Based on this distribution, Hospital Charlie will receive trauma kits, which is more kits than Hospital Alpha receives.

Show answer & explanation

Answer

Hospital Charlie receives 1,000 kits, which is 400 more than Hospital Alpha's 600 kits.

By adding the ratio parts (

3+4+5=12

) and dividing the total kits by this sum (

2,400 \div 12=200

), we find the value of one part. Multiplying by Charlie's ratio (

5

) gives 1,000 kits. Multiplying by Alpha's ratio (

3

) gives 600 kits. The difference is 400 kits.

Step-by-Step Solution

1

Calculate the total number of parts in the ratio.

3 + 4 + 5 = 12

total parts.

To find out how much one part of the ratio is worth, we first need to know the sum of all the parts.

2

Determine the value of a single part.

2,400 \div 12 = 200

kits per part.

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

3

Calculate the number of kits Hospital Charlie and Hospital Alpha receive.

Charlie receives

5 \times 200 = 1,000

kits. Alpha receives

3 \times 200 = 600

kits.

Multiply the number of parts each hospital has in the ratio by the value of a single part.

4

Calculate the difference between Charlie's and Alpha's shares.

1,000 - 600 = 400

kits.

The question asks for how many more kits Charlie receives compared to Alpha.

Key Concept

To divide a quantity in a given ratio, add the parts of the ratio to find the total parts, divide the total quantity by this sum to find the value of one part, and then multiply by the specific parts for each share.

Question 58Question →

A construction crew is pouring a foundation that requires $3.6$ tons of a custom gravel and sand mixture. If the mixture contains gravel and sand in a ratio of $5:4$ , how many pounds of sand are required for the foundation? ( $1$ ton $= 2,000$ pounds)

1,600

5,760

3,200

4,000

Show answer & explanation

Answer: $3,200$

Answer

The required amount of sand is

3,200

pounds.

The correct answer is found by first converting the total weight to pounds (

3.6 \times 2,000 = 7,200

pounds). The total number of parts in the ratio is

5 + 4 = 9

. Dividing the total weight by the total parts gives the weight of one part (

7,200 \div 9 = 800

pounds). Since the sand is the second component of the

5:4

ratio, it represents

4

parts. Multiplying the weight of one part by

4

gives

3,200

pounds.

Step-by-Step Solution

1

Convert the total weight of the mixture from tons to pounds.

3.6 \text{ tons} \times 2,000 \text{ pounds/ton} = 7,200 \text{ pounds}

The question asks for the final answer in pounds, so it is necessary to standardize the units first.

2

Determine the total number of parts in the ratio.

5 + 4 = 9 \text{ total parts}

To find the value of a single part, you must know how many equal parts make up the whole mixture.

3

Calculate the weight of one ratio part.

7,200 \text{ pounds} \div 9 \text{ parts} = 800 \text{ pounds/part}

Dividing the total weight by the total number of parts gives the weight of one proportional unit.

4

Calculate the total weight of the sand.

4 \text{ parts} \times 800 \text{ pounds/part} = 3,200 \text{ pounds}

The ratio of gravel to sand is

5:4

, meaning the sand accounts for exactly

4

of the

9

total parts.

Key Concept

Dividing in a Ratio

Question 59Question →

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

Show answer & explanation

Answer: $\$2,000$

Answer

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

.

Step-by-Step Solution

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.

Key Concept

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

Estimated Time:1m 0s

Question 60Question →

A quartermaster is allocating $2,100$ yards of heavy-duty canvas to manufacture temporary shelters, cot covers, and equipment tarps. The canvas is divided among these three projects in a ratio of $6:5:3$ , respectively. What is the difference, in yards, between the amount of canvas allocated for the temporary shelters and the amount allocated for the equipment tarps?

Show answer & explanation

Answer: 450

Answer

450

The correct answer is found by determining that the total ratio consists of 14 parts, meaning each part represents 150 yards (2100 / 14). The difference between the shelters (6 parts) and tarps (3 parts) is 3 parts, which equals 450 yards (3 * 150).

Step-by-Step Solution

1

Calculate the total number of parts in the ratio.

6 + 5 + 3 = 14

total parts.

To divide the total amount of canvas proportionally, we first need to determine the total number of equal parts.

2

Determine the value of a single part.

2,100 \div 14 = 150

yards per part.

Dividing the total yards by the total parts gives the amount of canvas for each ratio unit.

3

Calculate the difference in ratio parts between the shelters and the tarps.

6

parts (shelters) -

3

parts (tarps) =

3

parts difference.

We need the difference between the two allocations. Finding the difference in parts directly is the most efficient method.

4

Calculate the difference in yards.

3 \times 150 = 450

yards.

Multiplying the difference in ratio parts by the value of a single part yields the final answer.

Key Concept

Dividing a total quantity into a given ratio by finding the value of a single part.

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