AMC 8 · 2008 · #8

Grade 6 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation

graph-readingmean-median-mode-rangemulti-digit-arithmetic identify-subproblems ↑ Prerequisites: multi-digit-arithmeticgraph-reading

📏 Short solution 💡 2 insights 📊 Diagram

Problem

A bar chart shows the Boosters Club's candy sales for January, February, March, and April. Find the average sales per month, in dollars.

Pick an answer.

(A)

(B)

(C)

(D)

(E)

AMC 8 2008 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Visualize / Read the Diagram

The numbers we need are not written out — they are encoded in the heights of the bars. Tool #15 (Visualize / Read the Diagram) is the first move: read each bar against the gridlines at $40,$ 80, and $120 to pull out a number for each month. Tool #2 (Make a Systematic List) keeps the four month-by-month values lined up so we can add them with no mix-ups. After that the problem collapses to the Grade 6 mean formula: sum the four values and divide by 4.

1STEP 1

Read each bar against the $40/$ 80/ $120 gridlines; a bar halfway up a$ 40 gap sits $20 higher, so Jan = <span class="mk-a"><span class="hl-ask">$ 100 and Feb = $60.

Jan =

100, Feb =

60, Mar =

40, Apr =

120

2STEP 2

List all four sales and add — pairing $100+$ 120 and $60+$ 40 gives total = $320.

Total = 100 + 60 + 40 + 120 = 220 + 100 = $320

3STEP 3

Apply mean = total ÷ count: divide $320 by the 4 months to get <span class="mk-a"><span class="hl-ask">$ 80.

Average =

\frac{320}{4} =

80 → (D)

Answer

The four sales are

40,

60,

100,

120. The smallest is

40 and the largest is

120, so the average must lie strictly between

40 and

120. Our answer

80 sits right in that range. It also lines up with eyeballing the chart: two bars are below

80 (Mar and Feb) and two are above (

80) (Jan and Apr), which is exactly what you expect when

80 is the balance point.

💡Key takeaway

Read the bars, list the four numbers, add, and divide by 4 — the mean is just "total split fairly" across the months.

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