Problem 3 · 2014 AMC 8
Easy
Arithmetic & Operations
average-times-count
Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day for the first three days and an average of 44 pages per day for the next three days. She then finished the book by reading 10 pages on the last day. How many pages were in the book?
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Answer: B — 250 pages.
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Hint 1 of 2
An average is a stand-in for the real total: "36 pages a day for 3 days" carries the same total as 36 + 36 + 36. So average × days rebuilds each block's pages.
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Hint 2 of 2
Add the three blocks: first 3 days, next 3 days, and the final single day.
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Approach: average × count rebuilds each block's total
- First three days: 36 × 3 = 108 pages (the average undoes back into a total).
- Next three days: 44 × 3 = 132 pages.
- Total: 108 + 132 + 10 = 250.
- Key idea you'll reuse: total = average × count. Knowing any two of {total, average, count} gives the third — the same lever solves "find the missing test score" problems.
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