A military motor pool maintains a fleet of tactical trucks, transport vans, and passenger … — Armed Services Vocational Aptitude Battery (ASVAB)

A military motor pool maintains a fleet of tactical trucks, transport vans, and passenger cars in a ratio of $8:5:3$ . If there are exactly $112$ total vehicles in this fleet, how many transport vans does the motor pool maintain?

Answer: 35 vans

Answer

The motor pool maintains 35 transport vans.

The problem outlines a part-to-part-to-part ratio of

8:5:3

and a total quantity of

112

. To solve this, first add the parts of the ratio together (

8 + 5 + 3 = 16

). Next, divide the total quantity by the total ratio parts (

112 \div 16 = 7

) to determine that each 'part' represents

7

actual vehicles. Since the ratio for transport vans is the middle number (

5

), multiply

5

7

to correctly get

35

transport vans.

Step-by-Step Solution

Determine the total number of parts in the given ratio.

8 + 5 + 3 = 16

parts

Since the total number of vehicles in the fleet is given, we must find the total sum of the ratio parts to determine the size of a single part.

Calculate the exact value of a single ratio part.

112 \div 16 = 7

vehicles per part

Dividing the total quantity of vehicles by the total number of ratio parts gives the multiplier for the ratio.

Find the number of transport vans.

5 \times 7 = 35

transport vans

The ratio value specifically assigned to transport vans is

5

. Multiplying this by the value of one part gives the final count.

Key Concept

Solving part-to-whole ratio problems by establishing the total parts before finding specific component quantities.

Estimated Time:1m 0s

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