At the beginning of a quarter, the cost of raw material for a manufacturing plant was x do… — GRE General Test

At the beginning of a quarter, the cost of raw material for a manufacturing plant was $x$ dollars per ton. During the first month, the cost per ton increased by $15\%$ . During the second month, the cost per ton decreased by $20\%$ relative to the first month's price. If the cost per ton at the end of the second month was $\$552$ , what was the initial cost $x$ , in dollars?

Answer: 600 dollars

Answer

600

15\%

increase followed by a

20\%

decrease yields a combined multiplier of

(1 + 0.15)(1 - 0.20) = 1.15 \times 0.80 = 0.92

. Setting

0.92x = 552

gives

x = \frac{552}{0.92} = 600

Step-by-Step Solution

Calculate the price multiplier for the first month

Price after month 1 is

1.15x

15\%

increase scales the initial value by

(1 + 0.15) = 1.15

Calculate the price multiplier for the second month

Price after month 2 is

1.15x \times 0.80 = 0.92x

20\%

decrease applies to the new base price, scaling it by

(1 - 0.20) = 0.80

Solve for the initial price

x

x = 600

Divide the given final price of

\$552

by the overall multiplier

0.92

Key Concept

Successive Percent Changes and Base Shifts

Estimated Time:1m 30s

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