Problem 3 · 2020 Math Kangaroo
Easy
Algebra & Patterns
substitution
Miguel decided to solve three math problems a day. Eight days later, Daniel started solving five problems a day, until the two of them tied in the total number of problems solved. How many problems had each one solved by that day?
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Answer: C — 60
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Hint 1 of 2
When Daniel starts, Miguel already has an 8-day head start of solved problems.
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Hint 2 of 2
Set the two running totals equal and solve for the number of days Daniel has been solving.
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Approach: equate the two running totals
- By the time Daniel starts, Miguel has solved 3 × 8 = 24 problems.
- After Daniel works d days, Miguel has 24 + 3d and Daniel has 5d.
- Setting them equal: 24 + 3d = 5d, so 2d = 24 and d = 12.
- Each has then solved 5 × 12 = 60 problems, choice C.
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