Problem 2 · 2020 AMC 8
Easy
Arithmetic & Operations
total-then-divide
Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned $40 give to the others?
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Answer: C — $15.
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Hint 1 of 2
“Splitting equally” means everyone ends at the average. The $40 friend only gives away the part that's above average — you don't need to track who receives it.
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Hint 2 of 2
Find the fair share (the average), then the $40 friend hands over exactly the amount they sit above it.
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Approach: everyone ends at the average; give away the surplus
- Equal split means each friend ends with the average: (15 + 20 + 25 + 40) ÷ 4 = 100 ÷ 4 = $25.
- The $40 friend keeps $25 and gives away the surplus above average: $40 − $25 = $15.
- Why this transfers: in any “pool and share equally” problem, only the gaps from the average move — people above the average pay exactly their surplus, people below receive their shortfall. (Sanity check: those below average, $15 and $20, are short by $10 and $5 — together $15, matching what the $40 friend gives.)
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