Problem 9 · 1989 AJHSME
Medium
Ratios, Rates & Proportions
ratiopercent
There are 2 boys for every 3 girls in Ms. Johnson's math class. If there are 30 students in her class, what percent of them are boys?
Show answer
Answer: C — 40%.
Show hints
Hint 1 of 3
A ratio of 2 boys to 3 girls means the class splits into 2 + 3 = 5 equal-size groups. Boys aren't 2 out of 3 — they're 2 out of how many?
Still stuck? Show hint 2 →
Hint 2 of 3
Turn a ratio into a fraction-of-the-whole by adding the parts: boys are 2 of the 5 total parts.
Still stuck? Show hint 3 →
Hint 3 of 3
You don't even need the 30: boys are 2/5 of the class, and 2/5 is already a percent in disguise.
Show solution
Approach: add the ratio parts, then take the fraction of the whole
- The ratio 2 : 3 means 2 + 3 = 5 equal parts make up the class, and boys fill 2 of them — so boys are 2/5 of everyone.
- 2/5 = 40/100 = 40%. (Checking with the count: 30 ÷ 5 = 6 per part, boys = 2×6 = 12, and 12/30 = 40%.)
- Trap to avoid: 60% is the boys-to-girls comparison (2 is 2/3 of 3) — but the question asks boys as a slice of the whole class, which is 2/5. Always ask 'fraction of WHAT?' before converting to a percent.
Mark:
· log in to save