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Ratios, rates, and proportional relationships — ACT practice questions

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Practice 66 Ratios, rates, and proportional relationships questions in the app

What this topic is

Ratios, rates, and proportional relationships on the ACT Mathematics test cover unit conversions, inverse variation, and equations that set two fractions equal.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

The quantity $x$ varies inversely with $y$. When $x=6$, $y=8$. What is $x$ when $y=12$?

A3✗ Not this oneB4✓ CorrectC9✗ Not this oneD16✗ Not this one

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Answer: B — 4

For inverse variation, $xy$ is constant. Thus $6(8)=12x$, so $x=4$.

Question 2Mid

A delivery drone flies at a constant speed of 54 kilometers per hour. What is the drone’s speed in meters per second?

(Note: 1 kilometer = 1,000 meters)

A9✗ Not this oneB12✗ Not this oneC15✓ CorrectD18✗ Not this one

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Answer: C — 15

Convert: $54\cdot\dfrac{1000}{3600}=54\cdot\dfrac{5}{18}=15$ meters per second.

Question 3Mid

If $\dfrac{4x-y}{x+2y}=\dfrac{3}{5}$, then $\dfrac{x}{y}={}$ ?

A$\dfrac{3}{5}$✗ Not this oneB$\dfrac{11}{17}$✓ CorrectC$\dfrac{13}{17}$✗ Not this oneD$\dfrac{17}{11}$✗ Not this one

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Answer: B — $\dfrac{11}{17}$

Cross-multiplication gives $20x-5y=3x+6y$, so $17x=11y$ and $x/y=11/17$.

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