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Digital SAT · Solve it in Desmos

How to Solve Ratios and Proportions on Desmos (Digital SAT)

The calculator handles the cross-multiplication and division, handy on grid-ins. Arranging the proportion and choosing part-to-part versus part-to-whole are the calls you make.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for ratios and proportions

The Desmos steps

  1. 1

    Type the proportion

    Enter the two equal ratios as an equation with the unknown as x.

  2. 2

    Read the value

    Desmos returns the number that makes the ratios equal.

  3. 3

    Form the whole if needed

    For a part-to-whole answer, compute the total and build that ratio.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example
The ratio of the length of segment XYXY to the length of segment ZVZV is 6 to 1. If XYXY is 102 inches long, what is the length, in inches, of ZVZV?
1717
B
9696
C
108108
D
612612

A: Correct. From 61=102ZV\frac{6}{1} = \frac{102}{ZV}, 6⋅ZV=1026 \cdot ZV = 102, so ZV=17ZV = 17.

B: Incorrect. This subtracts 6 from 102 instead of dividing.

C: Incorrect. This adds 6 to 102 instead of dividing.

D: Incorrect. This multiplies 102 by 6 instead of dividing.

Explanation

Solve 61=102ZV\frac{6}{1} = \frac{102}{ZV}: ZV=17ZV = 17.

Medium example
A class contains 10 boys and 15 girls. What is the ratio of the number of boys to the total number of students in the class?
2 to 5
B
3 to 5
C
2 to 3
D
5 to 2

A: Correct. The total is 10+15=2510 + 15 = 25, so boys to total is 1025=25\frac{10}{25} = \frac{2}{5}.

B: Incorrect. This is the ratio of girls to the total, not boys to total.

C: Incorrect. This is the ratio of boys to girls, not boys to total.

D: Incorrect. This inverts the ratio of boys to total.

Explanation

Boys to total: 1025=25\frac{10}{25} = \frac{2}{5}, or 2 to 5.

Hard example

A traveler will convert 4,000 rupees to US dollars at a rate of 1 rupee = 0.012 US dollars. The exchange service charges a 3% fee on the converted dollar amount.

How many US dollars will the traveler receive after the 3% fee is applied?
46.5646.56
B
48.0048.00
C
333.33333.33
D
480.00480.00

A: Correct. Converting gives 4000×0.012=48.004000 \times 0.012 = 48.00; after the 3% fee, 48.00×0.97=46.5648.00 \times 0.97 = 46.56.

B: Incorrect. This is the amount before the 3% fee is subtracted.

C: Incorrect. This divides by the rate instead of multiplying.

D: Incorrect. This misplaces the decimal, using a rate of 0.12.

Explanation

Convert: 48.0048.00; apply fee: 48.00×0.97=46.5648.00 \times 0.97 = 46.56.

Detailed explanation

Multiplying 4,0004{,}000 rupees by 0.0120.012 gives 48.0048.00 dollars. The 3% fee removes 0.03×48.00=1.440.03 \times 48.00 = 1.44, leaving 48.00−1.44=46.5648.00 - 1.44 = 46.56. Skipping the fee gives 48.00, and misplacing the decimal or inverting the rate gives the larger values.

Try it with the calculator

Question 1easy

At an animal shelter, the ratio of cats to dogs is 4 to 3. If the shelter has 12 cats, how many dogs does it have?

Question 2easy

A car travels 120 miles using 4 gallons of gasoline. At this rate, how many miles can the car travel using 7 gallons of gasoline?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Desmos questions

Can Desmos solve ratios and proportions questions on the SAT?

The calculator handles the cross-multiplication and division, handy on grid-ins. Arranging the proportion and choosing part-to-part versus part-to-whole are the calls you make.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master ratios and proportions, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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