SHSAT SHSAT Word Problems 3

Question 1

A number is increased by 40% to get 70. What was the original number?

Accepted Answer

50

Answer

Let x be the original; x × 1.40 = 70; x = 70 ÷ 1.40 = 50.

Question 2

A pool is filled by two pipes. Pipe A fills it in 4 hours, Pipe B in 6 hours. How long together?

Accepted Answer

2.4 hours

Answer

Combined rate = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 per hour; time = 12/5 = 2.4 hours.

Question 3

A store reduces prices by 20%, then reduces the new price by another 10%. What is the total percent reduction from the original?

Accepted Answer

28%

Answer

After 20% off: 0.80 of original; after 10% off that: 0.80 × 0.90 = 0.72; reduction = 28%.

Question 4

James scored 85, 92, 78, and 95 on four tests. What score does he need on the fifth test to average 88?

Accepted Answer

90

Answer

Total needed = 88 × 5 = 440; current total = 85 + 92 + 78 + 95 = 350; need 440 − 350 = 90.

Question 5

A bicycle wheel has a diameter of 26 inches. How far does the bike travel in one full rotation of the wheel? (Use π ≈ 3.14)

Accepted Answer

81.64 in

Answer

Circumference = π × d = 3.14 × 26 = 81.64 inches per rotation.

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