Super-Hard SAT Data Analysis Question 16 | Free SAT Prep

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Question 16·50 Super-Hard SAT Problem Solving and Data Analysis Questions·Problem Solving and Data Analysis

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In March, an online bookstore's e-book sales, audiobook sales, and print-book sales accounted for $30\%$ , $25\%$ , and $45\%$ , respectively, of its total sales revenue.

From March to April, the number of e-books sold increased by $20\%$ , while the price of each e-book decreased by $10\%$ . The number of audiobooks sold did not change, while the price of each audiobook increased by $16\%$ . The number of print books sold decreased by $10\%$ .

The bookstore's total sales revenue in April was $10\%$ greater than its total sales revenue in March. If the price of each print book increased by $p\%$ from March to April, which choice gives the value of $p$ ?

For percentage problems involving several revenue categories, set the original total revenue to $100$ units so that each category's percentage becomes an actual amount. For each category, multiply its original revenue by every applicable change factor, such as $1.20$ for a $20\%$ increase or $0.90$ for a $10\%$ decrease. Do not add percentage changes when both quantity and price change; revenue changes are found by multiplying the factors.

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Choose a simple starting total

Treat the March total sales revenue as $100$ units. This converts the three given percentages directly into revenue amounts.

Account for both changes in e-book revenue

Revenue equals number sold times price. For e-books, multiply the March revenue by both the number-sold factor and the price factor.

Use the April total

After finding the April revenues for e-books and audiobooks, subtract their sum from the April total. The result is the required April print-book revenue.

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Use algebra first

Algebra is generally faster here because the March total can be set to $100$ and only one unknown remains.

Graph the total-revenue equation

Enter $y=30(1.2)(0.9)+25(1.16)+45(0.9)(1+x/100)$ and $y=110$ . The $x$ -coordinate of their intersection represents the required percentage increase in print-book price.

Step-by-step Explanation

Use a convenient revenue total

Let the total sales revenue in March be $100$ units. Then the March revenues were $30$ units for e-books, $25$ units for audiobooks, and $45$ units for print books. The April total is $110$ units because it is $10\%$ greater.

Find the April e-book and audiobook revenues

E-book revenue is multiplied by both $1.20$ for the number sold and $0.90$ for the price:

30(1.20)(0.90)=32.4

Audiobook revenue is multiplied by $1.16$ :

25(1.16)=29

Together, these categories account for $32.4+29=61.4$ units of April revenue.

Set the required print-book revenue

The print-book revenue in April must be

110-61.4=48.6

The $10\%$ decrease in the number of print books sold changes its March revenue to $45(0.90)=40.5$ units before the price increase. Therefore,

40.5\left(1+\frac{p}{100}\right)=48.6

Dividing by $40.5$ gives $1+\frac{p}{100}=1.2$ , so $p=20$ .

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Step-by-step Explanation

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