UTMA Word Problems and Applied Math 2 — Questions and Answers
Question 1: A rectangle has a perimeter of 54 cm and a length that is twice its width. What is the area?
- 162 cm² (Correct answer)
- 108 cm²
- 81 cm²
- 54 cm²
Correct answer: 162 cm²
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?
- $100
- $200
- $300 (Correct answer)
- $400
Correct answer: $300
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?
- 10:00 AM
- 11:00 AM (Correct answer)
- 12:00 PM
- 11:30 AM
Correct answer: 11:00 AM
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?
- 3 L
- 5 L (Correct answer)
- 7 L
- 10 L
Correct answer: 5 L
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?
- $16,000 (Correct answer)
- $18,000
- $20,000
- $24,000
Correct answer: $16,000
Commission = 2000 − 1200 = 800; Sales = 800 / 0.05 = $16,000.
Question 6: The ratio of boys to girls in a class is 3:4. If there are 28 students total, how many are boys?
- 9
- 12 (Correct answer)
- 16
- 21
Correct answer: 12
Boys = (3/7) × 28 = 12.
UTMA Word Problems and Applied Math 2
A rectangle has a perimeter of 54 cm and a length that is twice its width.
What is the area?