During a field exercise, a combat engineer platoon's daily fuel consumption increased by 2… — Armed Services Vocational Aptitude Battery (ASVAB)

During a field exercise, a combat engineer platoon's daily fuel consumption increased by $20\%$ in the first week, and then decreased by $25\%$ in the second week. If the final fuel consumption was $4,500$ gallons per day, what was the initial daily fuel consumption in gallons?

Answer: 5000 gallons

Answer

5000

The correct calculation requires treating the percentage changes as sequential multipliers. The initial amount increases by

20\%

(multiplier of

1.20

) and the new amount decreases by

25\%

(multiplier of

0.75

). The combined net multiplier is

1.20 \times 0.75 = 0.90

, meaning the final value is

90\%

of the initial value. To find the initial value, we divide the final amount (

4,500

) by

0.90

, which yields

5,000

Step-by-Step Solution

Determine the multipliers for the successive percentage changes.

20\%

increase is represented by

1.20

, and a

25\%

decrease is represented by

0.75

Successive percentage changes must be multiplied consecutively, not added together.

Set up an equation representing the net change.

x \times 1.20 \times 0.75 = 4500

The initial amount (

x

) multiplied by each successive change equals the final amount.

Calculate the combined multiplier.

1.20 \times 0.75 = 0.90

Simplifying the multipliers shows that the net change is a

10\%

decrease overall.

Solve the equation for the initial amount.

x = \frac{4500}{0.90} = 5000

Dividing the final consumption by the combined multiplier isolates

x

to find the original amount.

Key Concept

Successive Percentage Changes and Reverse Percentages

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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