Bluebook SAT Test Ratios, Rates, Proportional Relationships, and Units 6 — Questions and Answers
Question 1: A container is 25% full. After adding 18 liters, it is 70% full. What is the total capacity of the container in liters?
- 36
- 40 (Correct answer)
- 45
- 50
Correct answer: 40
18 liters fills 70% − 25% = 45% of capacity; capacity = 18 ÷ 0.45 = 40 liters.
Question 2: A car trip covers 1/4 of the distance in the first hour, and the remaining 90 miles in the next 2 hours. What was the total distance of the trip?
- 108 miles
- 112 miles
- 120 miles (Correct answer)
- 125 miles
Correct answer: 120 miles
The remaining 3/4 of the total equals 90 miles; total = 90 ÷ (3/4) = 120 miles.
Question 3: A 12% acid solution and a 30% acid solution are mixed to make 60 liters of an 18% acid solution. How many liters of the 12% solution are used?
- 30
- 36
- 40 (Correct answer)
- 45
Correct answer: 40
Let x = liters of 12% solution: 0.12x + 0.30(60−x) = 0.18(60) → −0.18x = −7.2 → x = 40.
Question 4: If the exchange rate is 1 USD = 0.85 EUR, how many USD would you receive for 51 EUR?
- 55
- 57
- 60 (Correct answer)
- 63
Correct answer: 60
USD = 51 ÷ 0.85 = 60.
Question 5: A photograph measures 4 inches by 6 inches. It is enlarged so that the longer side becomes 15 inches. What is the length of the shorter side of the enlarged photo?
- 8 in
- 9 in
- 10 in (Correct answer)
- 12 in
Correct answer: 10 in
Scale factor = 15 ÷ 6 = 2.5; shorter side = 4 × 2.5 = 10 inches.
Question 6: A worker earns $18.50 per hour for regular time and $27.75 per hour for overtime (any hours over 40 per week). How much does the worker earn in a week with 46 hours of work?
- $806.50
- $840.50
- $853.50
- $906.50 (Correct answer)
Correct answer: $906.50
Regular: 40 × $18.50 = $740; overtime: 6 × $27.75 = $166.50; total = $906.50.
Question 7: A scale model of a building is made at a ratio of 1:200. If the model is 0.45 meters tall, how tall is the actual building, in meters?
- 70 m
- 80 m
- 90 m (Correct answer)
- 100 m
Correct answer: 90 m
Actual height = 0.45 × 200 = 90 meters.
Bluebook SAT Test Ratios, Rates, Proportional Relationships, and Units 6
A container is 25% full.
After adding 18 liters, it is 70% full.
What is the total capacity of the container in liters?