Ratio, rate, and proportion word problems Practice Questions

Ratio, rate, and proportion word problems. Game on.

Ratio, rate, and proportion word problems is a grade 7 math skill aligned to Common Core standard 7.RP.A.2: recognize and represent proportional relationships between quantities. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 ratio, rate, and proportion word problems problems our math games drill.

CCSS 7.RP.A.210 questions in the bank

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Warm-upeasy

A passenger train traveled $348$ miles in $4$ hours at a constant speed. What was the train's speed, in miles per hour?

Speed = distance $\div$ time: $\dfrac{348}{4} = 87$ miles per hour.

Mid-gameeasy

At an animal shelter, the ratio of cats to dogs is $5$ to $8$ . If there are $35$ cats at the shelter, how many dogs are there?

Scale the ratio: $35$ cats is $7$ groups of $5$ , so dogs = $7 \times 8 = 56$ .

Mid-gameeasy

A cyclist rode $63$ kilometers in $1.5$ hours at a constant speed. What was the cyclist's speed, in kilometers per hour?

Speed = $\dfrac{63}{1.5} = 42$ kilometers per hour.

Mid-gameeasy

A paint mixture uses red and blue paint in a ratio of $4$ to $7$ . How many ounces of blue paint are needed to mix with $32$ ounces of red paint?

Scale the ratio: $32$ oz red is $8$ groups of $4$ , so blue paint = $8 \times 7 = 56$ ounces.

Mid-gamemedium

A recipe uses $3$ cups of flour to make $18$ muffins. At this rate, how many cups of flour are needed to make $30$ muffins?

Set up a proportion: $\dfrac{3}{18} = \dfrac{x}{30}$ , so $18x = 90$ and $x = 5$ cups.

Mid-gamemedium

A water tank held $12{,}500$ gallons of water. After leaking at a constant rate for $25$ minutes, the tank held $11{,}000$ gallons. How many gallons of water leaked from the tank each minute?

Water leaked: $12{,}500 - 11{,}000 = 1{,}500$ gallons in $25$ minutes. Rate: $\dfrac{1{,}500}{25} = 60$ gallons per minute.

Mid-gamemedium

Five identical printing presses can complete a job in $12$ hours. Working at the same rate, how many hours would it take $8$ of these presses to complete the same job?

Total work is fixed. Time with $8$ presses: $\dfrac{5 \times 12}{8} = \dfrac{60}{8} = 7.5$ hours.

Buzzer beatermedium

On a map, $1.5$ inches represents an actual distance of $36$ miles. At this scale, what is the actual distance, in miles, represented by $4$ inches on the map?

Scale: $\dfrac{36}{1.5} = 24$ miles per inch. For $4$ inches: $24 \times 4 = 96$ miles.

Ratio, rate, and proportion word problems. Game on.

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