Super-Hard SAT Math Question 139 | Free SAT Prep | Aniko

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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?

For “parts change by different percents but the total changes by a known percent” problems, set the original total to 100 and let one part be $x$ and the other $100-x$ . Convert percent changes to multipliers and use the new total to form an equation. If the question asks for a share in the new year, finish by dividing the updated part by the updated total and converting to a percent.

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Assume a total of 100 for 2025

Let the 2025 total revenue be 100 units. If online is $x$ , then in-store is $100-x$ .

Apply the percent changes as multipliers

Write 2026 online as $1.06x$ and 2026 in-store as $0.85(100-x)$ .

Use the 4% total decrease to solve for $x$

A 4% decrease from 100 means the 2026 total is 96. Set $1.06x + 0.85(100-x) = 96$ and solve for $x$ .

Compute the 2026 online share

After you find $x$ , compute 2026 online revenue $1.06x$ , then divide by the 2026 total (96) and convert to a percent.

Desmos Guide

Solve for the 2025 online amount $x$

Let $x$ be the 2025 online revenue out of 100.

In Desmos, graph:

$y = 1.06x + 0.85(100-x)$
$y = 96$

Read the intersection’s $x$ -value

Click the intersection point and record the $x$ -coordinate. That value is the 2025 online revenue (out of 100).

Compute the 2026 online percent

In Desmos, compute $100\cdot\frac{1.06x}{96}$ using the $x$ value from the intersection. Choose the closest answer choice.

Step-by-step Explanation

Represent 2025 revenue with a convenient total

Assume the company’s total revenue in 2025 was 100 units.

Let $x$ be the online revenue (in units) in 2025. Then the in-store revenue in 2025 was $100-x$ .

Write the 2026 revenues and use the total decrease

Online revenue increased by 6%, so 2026 online revenue is $1.06x$ .

In-store revenue decreased by 15%, so 2026 in-store revenue is $0.85(100-x)$ .

A 4% decrease from 100 means the 2026 total is $96$ , so:

\begin{aligned} 1.06x + 0.85(100-x) &= 96 \\ 1.06x + 85 - 0.85x &= 96 \\ 0.21x &= 11 \\ x &= \frac{1100}{21} \end{aligned}

Find online’s percent of the 2026 total

The 2026 online revenue is

1.06x = 1.06\left(\frac{1100}{21}\right).

So the fraction of 2026 total revenue (96 units) that is online is

\frac{1.06x}{96} = \frac{1.06\left(\frac{1100}{21}\right)}{96} \approx 0.5784.

Convert to a percent and select the closest choice

0.5784 = 57.84\%

The closest choice is 58%, so the correct answer is 58%.

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Step-by-step Explanation

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Step-by-step Explanation