Question 139·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

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A company’s revenue in 2025 came only from online sales and in-store sales. From 2025 to 2026, the company’s online sales revenue increased by 6% and its in-store sales revenue decreased by 15%. As a result, the company’s total revenue decreased by 4% from 2025 to 2026.

Approximately what percent of the company’s 2026 total revenue came from online sales?

A split-total percent-change question calls for a share ledger: write each category as a share of the original total, then apply its own change. If the starting shares are unknown, set the changed pieces equal to the given new total and use a Desmos regression to solve. To find a final share, divide by the new total, not the original one.

Hints

Hint 1
The two sources make up the entire 2025 total, so their starting shares add to $1$ . If online sales have a share of $s$ , what is the in-store share?
Hint 2
A percent-change factor tells you how much of an amount remains: a $6\%$ increase gives $1.06$ , while a $15\%$ decrease leaves $0.85$ . Multiply each 2025 share by its own factor.
Hint 3
A $4\%$ total decrease leaves $0.96$ per $1$ of 2025 revenue. After finding the starting split, compare online's 2026 amount with the 2026 total.

Step-by-step

Build a share ledger and solve in Desmos
Step 1
Write the 2025 shares
Count the 2025 total as $1$ . Let $s$ be online sales' share, or portion, of that total. Revenue came from only two sources, so the in-store share is $1-s$ .
Step 2
Turn the changes into a total-revenue equation
Online sales rise to $1.06s$ per $1$ of 2025 revenue. In-store sales fall to $0.85(1-s)$ . The total falls by $4\%$ , leaving $0.96$ per $1$ of 2025 revenue. Add the separately changed pieces to match that total:
$1.06s+0.85(1-s)=0.96.$
Step 3
Find the starting online share
In Desmos, type $1.06x_1+0.85(1-x_1)\sim0.96$ . Use $x_1$ for $s$ and $\sim$ for $=$ : a regression finds the value of $x_1$ that fits the equation. Under PARAMETERS, Desmos shows $x_1=0.5238095\ldots$ . That's the 2025 online share, not the share the question asks for.
Step 4
Find online revenue after its increase
Add $1.06x_1$ on the next Desmos line. It prints $0.555238\ldots$ . This contribution is 2026 online revenue measured against the 2025 total. Stopping here would use the wrong year's total for the requested share.
Step 5
Compare online revenue with the 2026 total
Add $100(1.06x_1)/0.96$ in Desmos. It prints $57.8373\ldots$ . For a 2026 share, divide the 2026 online amount by the 2026 total. So approximately $58\%$ of the company's 2026 revenue came from online sales. Choice B.

Question 139·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

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