A military transport unit has a fuel reserve of 420 gallons. On the first day of a field e… — Armed Services Vocational Aptitude Battery (ASVAB)

A military transport unit has a fuel reserve of $420$ gallons. On the first day of a field exercise, the unit consumes $\frac{2}{7}$ of the total reserve. On the second day, they consume $\frac{3}{5}$ of the remaining fuel. If the fuel that is left after the second day is divided equally among $4$ vehicles for a final patrol, how many gallons of fuel will each vehicle receive?

A
$12$
$30$ Answer
C
$61 \frac{1}{4}$
D
$120$

Answer

Each vehicle will receive

30

gallons of fuel.

To find the final amount per vehicle, calculate the remainder after each step. Day 1 consumes

120

gallons, leaving

300

gallons (

420 - 120

). Day 2 uses

\frac{3}{5}

300

, which is

180

gallons, leaving a final remainder of

120

gallons. Dividing these

120

gallons evenly among the

4

vehicles yields exactly

30

gallons per vehicle.

Step-by-Step Solution

Calculate the amount of fuel consumed on the first day and find the remaining balance.

First day consumption:

420 \times \frac{2}{7} = 120

gallons. Remaining fuel:

420 - 120 = 300

gallons.

The first day's usage is given as a fraction of the total initial reserve.

Calculate the amount of fuel consumed on the second day from the remaining balance, and find the new remainder.

Second day consumption:

300 \times \frac{3}{5} = 180

gallons. Remaining fuel:

300 - 180 = 120

gallons.

The problem explicitly states the second day's consumption is a fraction of the remaining fuel, not the original total.

Divide the final remaining fuel equally among the

4

vehicles.

120 \div 4 = 30

gallons per vehicle.

The total leftover fuel must be distributed evenly to find the specific amount allocated to each vehicle.

Key Concept

Applying sequential fraction multiplication to calculate remaining quantities in multi-step word problems.

Alternative Method

Use multiplication of the remaining fractions directly. After Day 1,

1 - \frac{2}{7} = \frac{5}{7}

of the fuel is left. After Day 2,

1 - \frac{3}{5} = \frac{2}{5}

of that remainder is left. The total fraction remaining of the original amount is

\frac{5}{7} \times \frac{2}{5} = \frac{2}{7}

. Multiply this by the original amount:

420 \times \frac{2}{7} = 120

gallons. Finally, divide by

4

to get

30

gallons per vehicle.

Estimated Time:1m 15s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Topics

More questions from this topic