Solve by Table/Function Regression

Percent Relationship Between Two Quantities on the SAT: Desmos Walkthrough

Anchor one quantity at 1, type each percent relationship as its own line, and let Desmos chain the arithmetic to the answer.

This lesson uses Desmos tables and regressions: drop the given values into a table, fit the model with a regression line, and read the constants straight off the fit.

Take this lesson interactively

A real SAT-style question

The positive number $a$ is $2,241 percent sign$ of the sum of the positive numbers $b$ and $c$ , and $b$ is $83 percent sign$ of $c$ . What percent of $b$ is $a$ ?

$23.24 percent sign$

$49.41 percent sign$

$2,324 percent sign$

$4,941 percent sign$

How to solve it in Desmos, step by step

The idea

Pick any value for c, let Desmos compute b and a from the percent relationships, then read a divided by b as a percent.

1
Step 1
Anchor c at 1 (the ratio answer is the same for any c). Type this line. Desmos shows c equals 1.
Type in Desmos
$c=1$
2
Step 2
b is 83 percent of c, which means 0.83 times c. Type this line. Desmos displays b equal to 0.83.
Type in Desmos
$b=0.83c$
3
Step 3
a is 2,241 percent of the sum of b and c, which means 22.41 times that sum. Type this line. Desmos displays a equal to 41.0103.
Type in Desmos
$a=22.41\left(b+c\right)$
4
Step 4
Ask what percent of b is a by dividing a by b and multiplying by 100. Type this line and read the value 4941, which is choice D, 4,941 percent.
Type in Desmos
$\frac{a}{b}\cdot100$

The answer is D.

$4,941 percent sign$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

The positive number

a

1{,}620

percent of the sum of the positive numbers

b

and

c

, and

b

80

percent of

c

. What percent of

b

a

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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Percent Relationship Between Two Quantities on the SAT: Desmos Walkthrough

A real SAT-style question

How to solve it in Desmos, step by step

The idea

Step 1

Step 2

Step 3

Step 4

Now you try one

Practice this with a live Desmos calculator

More Desmos SAT lessons