🇺🇸 AMC 8 ⇄ switch contest
2013 AMC 8

Problem 4

Problem 4 · 2013 AMC 8 Easy
Algebra & Patterns find-share-then-total

Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?

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Answer: C — $140.
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Hint 1 of 2
The seven $2.50 extras didn't vanish — together they exactly paid off Judi's one share. So 7 × $2.50 is one person's share of the bill.
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Hint 2 of 2
Find the size of one equal part first, then scale up to the whole. One share × (number of shares) = total.
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Approach: find one share, then multiply by 8
  1. The 7 extra payments covered exactly Judi's portion, so one person's share = 7 × $2.50 = $17.50. (That's the key reframe: the extras add up to one full share.)
  2. Everyone owed the same share, and there are 8 people, so the total bill = 8 × $17.50 = $140.
  3. Sanity check: $17.50 per person feels right for a restaurant, and 8 of them lands at $140 — matching a choice.
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