UTMA Word Problems and Applied Math

Question 1

A car travels 240 miles in 4 hours. What is its average speed in miles per hour?

Accepted Answer

60 mph

Answer

Speed = Distance / Time = 240 / 4 = 60 mph.

Question 2

A store marks up a jacket by 25% from its cost of $80. What is the selling price?

Accepted Answer

$100

Answer

Markup = 0.25 × 80 = $20; Selling price = 80 + 20 = $100.

Question 3

Two pipes fill a tank in 6 and 12 hours respectively. How long do they take working together?

Accepted Answer

4 hours

Answer

Combined rate = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4; time = 4 hours.

Question 4

Maria is 3 times as old as Tom. In 5 years, she will be twice Tom's age. How old is Tom now?

Accepted Answer

5

Answer

Let Tom = t; Maria = 3t. In 5 years: 3t+5 = 2(t+5) → t = 5.

Question 5

A 10-meter ladder leans against a wall. If the base is 6 meters from the wall, how high does it reach?

Accepted Answer

8 m

Answer

Using the Pythagorean theorem: h² = 10² − 6² = 100 − 36 = 64, so h = 8 m.

UTMA - University of Toronto Math Assessment Practice Test