Bluebook SAT Test Ratios, Rates, Proportional Relationships, and Units 13

Question 1

A container that holds 5 gallons is 40% full. How many more gallons must be added to make it 90% full?

Accepted Answer

2.5 gallons

Answer

Current = 0.40 × 5 = 2 gal; target = 0.90 × 5 = 4.5 gal; add 4.5 − 2 = 2.5 gallons.

Question 2

A jogger runs at 7.5 mph. A cyclist rides 3 times as fast. How many miles can the cyclist travel in 40 minutes?

Accepted Answer

15 miles

Answer

Cyclist speed = 3 × 7.5 = 22.5 mph; distance in 40 min = 22.5 × (40/60) = 22.5 × 2/3 = 15 miles.

Question 3

The lengths of the sides of a rectangle are in the ratio 5:8. If the perimeter is 104 cm, what is the area of the rectangle?

Accepted Answer

640 cm²

Answer

2(5k + 8k) = 26k = 104, so k = 4; sides = 20 cm and 32 cm; area = 20 × 32 = 640 cm².

Question 4

A photograph 4 in × 5 in is enlarged proportionally so the longer side becomes 20 in. What is the length of the shorter side?

Accepted Answer

16 inches

Answer

Scale factor = 20 ÷ 5 = 4; shorter side = 4 × 4 = 16 inches.

Question 5

A 180-gram snack package is 45% carbohydrates. If the serving size is 30 grams, how many grams of carbohydrates are in one serving?

Accepted Answer

13.5 grams

Answer

45% of 30 grams = 0.45 × 30 = 13.5 grams.

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