Problem 13 · 2009 Math Kangaroo
Medium
Algebra & Patterns
substitution
A dance group has 39 boys and 23 girls. Every week 6 more boys and 8 more girls join the group. After some weeks there will be the same number of boys as girls. How many boys and girls will be in the dance group then?
Show answer
Answer: D — 174
Show hints
Hint 1 of 2
At the start there are more boys than girls — how big is that gap?
Still stuck? Show hint 2 →
Hint 2 of 2
Each week girls gain 8 but boys gain only 6, so watch how much the gap shrinks every week.
Show solution
Approach: close the gap week by week
- At the start there are 39 − 23 = 16 more boys than girls.
- Each week the girls gain 8 and the boys gain 6, so the gap shrinks by 2 every week.
- To close a gap of 16 at 2 per week takes 16 ÷ 2 = 8 weeks; then boys = 39 + 8×6 = 87 and girls = 23 + 8×8 = 87.
- Together that is 87 + 87 = 174 — answer D.
Algebra version (older kids)
Set 39 + 6w = 23 + 8w, so 16 = 2w and w = 8, giving 174.
Mark:
· log in to save