🇺🇸 AMC 8 ⇄ switch contest
1988 AJHSME

Problem 20

Problem 20 · 1988 AJHSME Hard
Fractions, Decimals & Percents percent-of-whole
Figure for AJHSME 1988 Problem 20
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Answer: C — 125.
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Hint 1 of 2
You're told the *part* (45 cups) and the *percent* it represents (36%); you want the *whole*. Since 45 is only 36% of the maker, the full capacity must be larger than 45 — which choices does that already rule out?
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Hint 2 of 2
If 36% of the full amount is 45, then full × 0.36 = 45. Undo the multiply: divide 45 by 0.36.
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Approach: the part ÷ its percent gives the whole
  1. 45 cups is 36% of the full pot, so Full × 0.36 = 45, giving Full = 45 ⁄ 0.36 = 4500 ⁄ 36 = 125 cups.
  2. Intuition check: if 36% is 45 cups, then each 1% is 45 ⁄ 36 = 1.25 cups, so the full 100% is 1.25 × 100 = 125 cups. Same answer, and it's comfortably bigger than 45 as expected.
  3. Why this transfers: 'this part is P% of the whole' always rearranges to whole = part ÷ (P as a decimal). Finding the 'per 1%' amount first and scaling to 100 is a handy mental shortcut for the same idea.
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