Problem 5 · 2021 Math Kangaroo
Medium
Logic & Word Problems
substitutionsum-constraint
The halftime score of a handball match was 9:14, so the visiting team was leading by five goals. After instructions from the coach, the home team dominated the second half and scored twice as many goals as their opponents. The home team won the match by one goal. What was the final score of the match?
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Answer: B — 21:20
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Hint 1 of 2
Let the visitors score x in the second half; then the home team scores 2x.
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Hint 2 of 2
Write 'home wins by one goal' as an equation in x and solve.
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Approach: set up one equation for the second half
- Halftime is home 9, visitors 14. Let visitors score x more; the home team scores 2x more.
- Final: home 9+2x, visitors 14+x, and home wins by one: 9+2x = (14+x)+1.
- Solving gives x = 6, so home = 21 and visitors = 20.
- Final score 21:20, choice (B).
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