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Problem Solving And Data Analysis · Ratios Rates And Proportions

SAT Ratios Rates And Proportions Practice Questions (Free + Explanations) | Quiz 7

Question 12345 of 5

Question 1 of 5

A cylindrical water tank is being filled at a constant rate. After 6 minutes, the tank contains 180 gallons of water. At this rate, how many gallons of water will be in the tank when the water level has risen from 2 feet to 5 feet, assuming the tank was empty when filling began?

Explanation

Because the tank is cylindrical, its cross-sectional area is constant, so the volume of water is proportional to the height of the water level. If 2 feet of water corresponds to 180 gallons, then 1 foot corresponds to gallons. A water level of 5 feet therefore corresponds to gallons. So the correct answer is .

Concept summary

In a cylinder, volume is proportional to height because the base area stays constant. A ratio can be used to scale from one height and volume pair to another.

Question 2 of 5

A community garden uses a water tank to irrigate its plants. At a constant rate, the tank dispenses 18 gallons of water in 12 minutes. At this same rate, how many gallons of water will the tank dispense in 35 minutes?

Explanation

First find the unit rate in gallons per minute: gallons per minute. Then multiply by 35 minutes: . Therefore, the tank will dispense gallons in 35 minutes.

Concept summary

Use proportional reasoning by finding a unit rate first, then apply that rate to the new amount of time.

Question 3 of 5

A lab technician uses a concentrated cleaning solution and water to make a diluted mixture. The ratio of concentrate to water in the diluted mixture must be . If the technician has already poured 24 ounces of concentrate into a container, how many ounces of water should be added so that the final mixture has the correct ratio?

Explanation

The ratio of concentrate to water must be . Since 24 ounces of concentrate are already in the container, set up a proportion: , where is the number of ounces of water. Cross-multiply: . Then divide by 3: . So 136 ounces of water should be added.

Concept summary

Use ratios by matching corresponding parts with a proportion. If one part of a ratio is known, scale both parts by the same factor to find the missing quantity.

Question 4 of 5

The graph of a proportional relationship between the number of miles driven, , and the amount of gasoline used, , passes through the point . Based on this graph, how many miles are driven per gallon of gasoline?

Explanation

In a proportional relationship, the ratio between the variables is constant. The point means 120 miles are driven using 4 gallons of gasoline. To find miles per gallon, divide miles by gallons: . So the car travels 30 miles for each gallon of gasoline.

Concept summary

For a proportional relationship shown by a point on a graph, a unit rate is found by dividing one quantity by the other in the order requested.

Question 5 of 5

A school cafeteria makes a snack mix by combining peanuts and raisins. Peanuts cost 7 per pound. On one day, the cafeteria used 30 pounds of snack mix that had a total cost of

Explanation

Let be the number of pounds of peanuts and be the number of pounds of raisins. The total weight gives the equation . The total cost gives the equation . Substitute into the cost equation: . Then , so . Subtract 120 from both sides: . Divide by 3 to get . Therefore, 12 pounds of raisins were used.

Concept summary

Use a system of equations when two quantities are related by both a total amount and a total cost. One equation represents the total quantity, and the other represents the weighted cost.

Your results

0of 5 correct

Estimated SAT Math band

500-550

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

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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