UTMA Word Problems and Applied Math 2

Question 1

A rectangle has a perimeter of 54 cm and a length that is twice its width. What is the area?

Accepted Answer

162 cm²

Answer

2(l+w) = 54; l = 2w → 2(3w) = 54 → w = 9, l = 18; Area = 18×9 = 162 cm².

Question 2

A bank account earns 4% simple annual interest. How much interest is earned on $2,500 in 3 years?

Accepted Answer

$300

Answer

Simple interest = P × r × t = 2500 × 0.04 × 3 = $300.

Question 3

Train A leaves at 8:00 AM at 60 km/h and Train B leaves the same station at 9:00 AM at 90 km/h in the same direction. When does Train B catch Train A?

Accepted Answer

11:00 AM

Answer

Train A has a 60 km head start. B closes at 30 km/h: 60/30 = 2 hours after 9 AM = 11 AM.

Question 4

A solution is 30% salt. How many liters of pure water must be added to 10 L of this solution to make it 20% salt?

Accepted Answer

5 L

Answer

Salt = 3 L; 3/(10+x) = 0.20 → 3 = 2 + 0.2x → x = 5 L.

Question 5

A salesperson earns a base salary of $1,200/month plus 5% commission on sales. If they earned $2,000 last month, what were their total sales?

Accepted Answer

$16,000

Answer

Commission = 2000 − 1200 = 800; Sales = 800 / 0.05 = $16,000.

UTMA - University of Toronto Math Assessment Practice Test

UTMA - University of Toronto Math Assessment Practice Test

UTMA Word Problems and Applied Math 2