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Problem Solving And Data Analysis · Ratios Rates And Proportions

SAT Ratios Rates And Proportions Practice Questions (Free + Explanations) | Quiz 5

Question 12345 of 5

Question 1 of 5

The table shows the amount of blue paint and white paint used to make several batches of the same shade of light blue paint.

If a larger batch is made with 24 cups of white paint and the same shade is maintained, how many cups of blue paint are needed?

Explanation

The ratio of blue paint to white paint is constant for the same shade. From the table, , so the ratio is . For a batch with 24 cups of white paint, let be the number of cups of blue paint. Then

Multiply both sides by 24:

So 14.4 cups of blue paint are needed.

Concept summary

In a proportional relationship, equivalent ratios can be used to scale quantities up or down. Set up a proportion using matching parts of the ratio before solving.

Question 2 of 5

A recipe uses a ratio of 3 cups of flour to 2 cups of sugar. A baker says, "If I use 15 cups of flour and 12 cups of sugar, then the mixture must be too sweet." Which statement must be true?

Explanation

The original ratio of flour to sugar is . To keep the same ratio when using 15 cups of flour, multiply both parts of the ratio by 5, since . That gives cups of sugar. But the baker uses 12 cups of sugar, which is 2 cups more than needed to keep the ratio the same. Therefore, the mixture has a greater proportion of sugar than the original recipe, so it must be too sweet compared with the original. Choice A is correct.

Concept summary

To decide whether two quantities are proportional, compare whether both parts of the ratio are scaled by the same factor or find the expected amount using equivalent ratios.

Question 3 of 5

A cylindrical water tank is being drained at a constant rate. When the water is 18 inches deep, the tank contains 54 gallons of water. If the tank has the same diameter throughout, how many gallons of water does it contain when the water is 30 inches deep?

Explanation

Because the tank is cylindrical and has the same diameter throughout, the volume of water is directly proportional to the water depth. So the ratio of gallons to inches stays constant. At 18 inches, the tank contains 54 gallons, so there are gallons per inch of depth. At 30 inches, the amount of water is gallons. Therefore, the correct answer is .

Concept summary

In a cylinder with constant diameter, volume is proportional to height or depth. Set up a proportion using the ratio of volume to depth.

Question 4 of 5

A food company is testing a new snack mix recipe. The table shows the number of cups of pretzels and the total number of cups of snack mix made when the recipe is followed exactly.

Pretzels (cups) | Total snack mix (cups)
3 | 8
6 | 16
9 | 24

If the company uses 15 cups of pretzels and keeps the recipe the same, how many cups of peanuts will be in the snack mix?

Explanation

From the table, 3 cups of pretzels make 8 cups of total mix, so the recipe uses a constant ratio. That means the total mix is times the amount of pretzels. For 15 cups of pretzels, the total mix will be cups. The peanuts are the part of the mix that is not pretzels, so cups of peanuts . Therefore, the correct answer is 25.

Concept summary

Use equivalent ratios in a table to scale a recipe, then subtract a known part from the total to find the remaining part.

Question 5 of 5

A recipe uses flour and sugar in a ratio of . A baker has already mixed 18 cups of sugar with some flour and wants the final mixture to keep the same flour-to-sugar ratio. If the baker then adds 7 more cups of flour, the mixture will have exactly the correct ratio. How many cups of flour were in the mixture before the 7 cups were added?

Explanation

The final flour-to-sugar ratio must be . Since there are 18 cups of sugar, the amount of flour in the final mixture must satisfy

Solving gives

So after the extra 7 cups are added, there are 30 cups of flour. Therefore, before those 7 cups were added, there were

cups of flour. So the correct answer is .

Concept summary

Use a proportion to connect the given ratio to one known quantity, then work backward if the question asks for an earlier amount.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice