Problem Solving: Word Problems Flashcards

The sum of three consecutive even integers is 90. What is the largest of the three integers?

Answer: 32

Let the integers be n, n+2, n+4; then 3n + 6 = 90, so n = 28 and the largest is 32.

A student scored 85, 90, 78, and 92 on four tests. What score is needed on the fifth test to average exactly 88?

Answer: 95

Required total = 5 × 88 = 440; current total = 345; fifth score = 440 − 345 = 95.

A 40-liter mixture is 25% alcohol. How many liters of pure alcohol must be added to make the mixture 40% alcohol?

Answer: 10 liters

Setting up (10 + x)/(40 + x) = 0.40 and solving gives x = 10 liters.

A cyclist averages 12 mph uphill and 18 mph downhill over equal distances each way. What is the average speed for the entire round trip?

Answer: 14.4 mph

Use the harmonic mean: 2 × 12 × 18 / (12 + 18) = 432 / 30 = 14.4 mph.

A map has a scale of 1 inch = 25 miles. Two cities are 3.5 inches apart on the map. What is the actual distance between them?

Answer: 87.5 miles

Actual distance = 3.5 × 25 = 87.5 miles.

A 13-foot ladder leans against a wall with its base 5 feet from the wall. How high up the wall does the ladder reach?

Answer: 12 feet

Using the Pythagorean theorem: height = √(13² − 5²) = √(169 − 25) = √144 = 12 feet.

Pipe A fills a tank in 3 hours; Pipe B drains it in 5 hours. With both pipes open, how long does it take to fill an empty tank?

Answer: 7.5 hours

Net rate = 1/3 − 1/5 = 2/15 per hour, so time = 15/2 = 7.5 hours.