Read the scenario and determine the final quantity. Fill in the blank with the correct num… — Armed Services Vocational Aptitude Battery (ASVAB)

Read the scenario and determine the final quantity. Fill in the blank with the correct numeric value.

Answer:A military engineering unit has a stockpile of

315

tons of crushed rock. They use

\frac{4}{9}

of the total stockpile to reinforce a main supply route. The unit commander then orders the remaining crushed rock to be divided into equal truckloads of

12 \frac{1}{2}

tons each for distribution to forward operating bases. The unit will be able to distribute exactly 【14】 full truckloads to the forward bases.

Answer

By first finding the remaining amount of crushed rock (

175

tons) and then dividing it by the size of each load (

12 \frac{1}{2}

tons), we determine there are exactly

14

truckloads.

Step-by-Step Solution

Determine the fraction of the stockpile that remains after the main supply route is reinforced.

1 - \frac{4}{9} = \frac{5}{9}

The truckloads are created from the remaining crushed rock, not the amount used for the main supply route.

Calculate the total weight of the remaining crushed rock.

315 \times \frac{5}{9} = \frac{315 \times 5}{9} = 35 \times 5 = 175

tons

This gives the exact quantity of rock available to be divided into individual truckloads.

Determine the number of truckloads by dividing the remaining weight by the weight per truckload.

175 \div 12 \frac{1}{2} = 175 \div \frac{25}{2} = 175 \times \frac{2}{25} = 7 \times 2 = 14

truckloads

Dividing the total available weight by the capacity of each load yields the total number of loads.

Key Concept

Solving multi-step word problems involving multiplication of whole numbers by fractions and division by mixed numbers.

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