At the beginning of a school year, a bookstore had 250 copies of a textbook in stock. Duri… — SAT

At the beginning of a school year, a bookstore had $250$ copies of a textbook in stock. During the first week of classes, the bookstore sold $30\%$ of the textbooks in stock. During the second week, a new shipment increased the number of textbooks in stock by $40\%$ of the number of textbooks in stock at the end of the first week. How many copies of the textbook were in stock at the end of the second week?

Answer: 245 copies

Answer

245

To find the final quantity, we must calculate the successive percentage changes sequentially. First, a

30\%

decrease on the initial

250

textbooks leaves

70\%

of the stock:

250 \times 0.70 = 175

. Second, a

40\%

increase on this new amount of

175

textbooks results in

175 \times 1.40 = 245

textbooks in stock at the end of the second week.

Step-by-Step Solution

Find the number of textbooks remaining after the first week's sales.

175

Selling

30\%

of the

250

textbooks leaves

70\%

of them:

250 \times (1 - 0.30) = 175

Find the total number of textbooks in stock after the second week's shipment increase.

245

An increase of

40\%

on the

175

remaining textbooks results in

140\%

of that amount:

175 \times (1 + 0.40) = 245

Key Concept

Applying consecutive percent decreases and increases to changing base values.

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