Competition · AMC preparation · step 4 of 4

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)
60
(B)
70
(C)
75
(D)
80
(E)
85

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 40,40,80, 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

Read each bar against the $40/$80/$120 gridlines; a bar halfway up a $40 gap sits $20 higher, so Jan = $100 and Feb = $60.

Jan = 100,Feb=100, Feb =60, Mar = 40,Apr=40, Apr =120
2STEP 2

Add the four months

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

Divide by 4

Apply mean = total ÷ count: divide $320 by the 4 months to get $80.

Average = 320/4=320/4 =80 → (D)
Answer
80
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.

  • Read each bar
  • Add the four months
  • Divide by 4

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