Problem 7 · 2015 Math Kangaroo
Easy
Algebra & Patterns
substitution
There are 33 teenagers in a class. Their favourite subjects are either computing, PE or both. Three of them like both subjects. There are twice as many teenagers who only like computing as teenagers who like PE only. How many of them like computing?
Show answer
Answer: E — 23
Show hints
Hint 1 of 2
Split the class into computing-only, PE-only, and both, and write the total.
Still stuck? Show hint 2 →
Hint 2 of 2
Let PE-only be p; then computing-only is 2p, and 3 + p + 2p = 33.
Show solution
Approach: set up parts of a Venn split
- Let PE-only = p, so computing-only = 2p, and both = 3.
- 3 + p + 2p = 33 gives 3p = 30, so p = 10.
- Computing-only = 20; those who like computing = 20 + 3 (the 'both') = 23.
Mark:
· log in to save