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2009 Math Kangaroo

Problem 9

Problem 9 · 2009 Math Kangaroo Medium
Algebra & Patterns arithmetic-sequence

In a dance group there are 25 boys and 19 girls. Every week 2 more boys and 3 more girls join the group. After how many weeks will there be the same number of boys as girls in the dance group?

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Answer: A — 6
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Hint 1 of 2
The girls start behind but gain on the boys each week.
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Hint 2 of 2
How many more girls than boys arrive each week, and how big is the gap to close?
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Approach: close the gap one week at a time
  1. At the start there are 25 boys and 19 girls: 6 more boys.
  2. Each week 3 girls and 2 boys join, so the girls gain 1 on the boys per week.
  3. To erase the gap of 6, that takes 6 weeks.
  4. After 6 weeks the numbers are equal (37 each).
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