Problem 16 · 1985 AJHSME
Hard
Ratios, Rates & Proportions
ratio-parts
The ratio of boys to girls in Mr. Brown's math class is 2 : 3. If there are 30 students in the class, how many more girls than boys are in the class?
Show answer
Answer: D — 6.
Show hints
Hint 1 of 2
Think of the ratio 2 : 3 as dividing the class into equal-size 'parts' — 2 parts of boys and 3 parts of girls. How many parts is that all together, and how big is each one?
Still stuck? Show hint 2 →
Hint 2 of 2
Add the ratio numbers to get the total parts (2 + 3 = 5), divide the class by that to size one part, then read off whatever the question asks. Here 'how many more girls' is just the part-difference (3 − 2 = 1 part).
Show solution
Approach: size of one part times the difference of parts
- The ratio splits the class into 2 + 3 = 5 equal parts, so each part = 30 ⁄ 5 = 6 students.
- Girls (3 parts) outnumber boys (2 parts) by exactly 1 part: extra girls = 1 × 6 = 6.
- Spot the trap: '6' is the difference of parts (3 − 2 = 1 part), NOT the count of girls (which is 18) or 2 parts (which is 10, a tempting wrong answer). Always match the question to the right number of parts.
Mark:
· log in to save