AMC 8 · 2014 · #3

Grade 6 arithmetic
mean-median-mode-rangemulti-digit-arithmetic identify-subproblems ↑ Prerequisites: multi-digit-arithmeticmean-median-mode-range
📏 Short solution 💡 2 insights
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Problem
Isabella read a book over 7 days. For the first 3 days she averaged 36 pages per day, for the next 3 days she averaged 44 pages per day, and on the last day she finished the book by reading 10 pages. How many pages were in the book in total?

Pick an answer.

(A)
240
(B)
250
(C)
260
(D)
270
(E)
280

AMC 8 2014 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve
Strategy Identify Subproblems

The week splits naturally into three pieces — Days 1–3, Days 4–6, and Day 7 — with different reading paces, so Tool #7 (Identify Subproblems) is the cleanest entry: compute the page total for each piece, then add. Tool #2 (Find a Pattern) is the supporting move: noticing that the first two pieces share the same length (3 days) lets us factor and write 3 × (36 + 44) + 10 instead of doing two separate multiplications, which is faster and easier to check.

1STEP 1

Average × days recovers a block total, so the first 3 days come to 108 pages.

36 × 3 = 108 pages
2STEP 2

The same move on the next 3 days: 44 pages/day gives 132 pages.

44 × 3 = 132 pages
3STEP 3

Add the three pieces — 108, 132, and the last day's 10 — for the whole book: 250 pages.

108 + 132 + 10 = 250 pages → (B)
4STEP 4

Cross-check: both blocks are 3 days, so factor once — 3 × (36 + 44) + 10 = 250.

3 × (36 + 44) + 10 = 3 × 80 + 10 = 240 + 10 = 250
Answer
250
Across the full 7 days she reads 250 pages, which is an overall average of 2507\frac{250}{7} ≈ 35.7 pages per day. That sits sensibly between the 36 pages/day pace and the 44 pages/day pace — pulled down by the small 10-page final day. A typical school book of around 250 pages is also realistic for a one-week assignment.
💡Key takeaway

This AMC 8 problem only needs the Grade 6 idea that "average × count = total" — split the week into pieces, multiply each piece, then add.