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

0 / 50 Questions completed

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 $p$ ?

When several categories make up a total and each changes differently, use a weighted average of the revenue multipliers. Treat the original revenue shares as starting amounts, then multiply each by its number-sold and price multipliers. Add the new amounts and use a Desmos regression to find the missing percent. Don't add changes in quantity and price; both affect the same revenue.

Hints

Hint 1
Use March's shares as amounts out of an imagined $100 total. These are starting amounts, not shares of April's total. How much would April revenue be if the overall increase were applied to that $100?
Hint 2
Revenue is number sold times price. If both change, turn each percent change into a multiplier and use both. What two multipliers act on e-book revenue?
Hint 3
The print-book count falls before you account for its unknown price increase. Its new quantity leaves 90% of the old print-book revenue at the old price. What multiplier represents a price increase of $p\%$ ?

Step-by-step

Build a revenue-share ledger
Step 1
Choose a convenient March total
Take March's total revenue as $100, so the e-book, audiobook, and print-book shares are $30, $25, and $45. The actual total doesn't matter: scaling every revenue amount together won't change the percent increase in print-book price.
Step 2
Find April's e-book revenue
Revenue is the number sold times the price. The e-book count rises by $20\%$ , giving a $1.20$ multiplier; its price falls by $10\%$ , giving a $0.90$ multiplier. Multiply both changes to find the revenue change: type $30(1.20)(0.90)$ . Desmos returns $32.4$ , so e-books contribute $32.40 in April for our $100 March total.
Step 3
Find April's audiobook revenue
The audiobook count doesn't change, so only its price gets a multiplier. Type $25(1.16)$ ; Desmos returns $29$ . That is the audiobook contribution to April revenue.
Step 4
Account for fewer print books
Selling $10\%$ fewer print books leaves $90\%$ of the old count. Type $45(0.90)$ ; Desmos returns $40.5$ . This is what print-book revenue would be at the old price. Its price increase still needs to be applied.
Step 5
Make the April categories add to the total
A price increase of $p\%$ makes the new print-book price $1+\frac{p}{100}$ times the old price. Use the whole new price multiplier, not just the amount added. April's total is $10\%$ above March's $100, or $110, so the three April contributions add to $32.4+29+40.5\left(1+\frac{p}{100}\right)=110$ .
Step 6
Solve for the print-book price increase
Use a Desmos regression to find the value that makes both sides equal. Replace $p$ with $x_1$ and $=$ with $\sim$ ; Desmos treats $x_1$ as a value to find rather than a graph variable. Type $32.4+29+40.5(1+x_1/100)\sim110$ . Under PARAMETERS, Desmos shows $x_1=20$ . So the print-book price increased by $20\%$ . Choice D.

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

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this