AMC 8 · 2002 · #7

Grade 6 rate-ratio

Archetype Arithmetic Expression Decomposition └ Sub-archetype Linear Rate Accumulation

percentagegraph-readingfraction-arithmetic identify-subproblems ↑ Prerequisites: fraction-arithmeticpercentage

📏 Short solution 💡 2 insights 📊 Diagram

Problem

Mrs. Sawyer's class voted between five kinds of candy (A through E), and the results are shown on a bar graph. Reading the bars: A = 6, B = 8, C = 4, D = 2, E = 5 students. What percent of the class chose candy E?

Pick an answer.

(A)

(B)

(C)

(D)

(E)

AMC 8 2002 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Identify Subproblems

The work splits cleanly into Tool #7 subproblems: (1) read the five bar heights, (2) add them to get the class total, (3) form the fraction $\frac{E}{\text{total}}$ and convert to a percent. Tool #5 (Look for a Pattern) finishes the last step quickly — 5 out of 25 is the familiar $\frac{1}{5}$ = 20% pattern, so no long division is needed.

1STEP 1

Read the five bar heights off the graph; candy E's bar reaches 5 students.

A = 6, B = 8, C = 4, D = 2, E = 5

2STEP 2

Add the five bar heights, counting each student once — the class totals 25 students.

6 + 8 + 4 + 2 + 5 = 25 students

3STEP 3

Write E's share as a fraction over the class total: $\frac{5}{25}$ × 100%.

percent for E =

\frac{5}{25}

× 100%

4STEP 4

Simplify $\frac{5}{25}$ to $\frac{1}{5}$ , the well-known 20% pattern → (E).

\frac{5}{25}

× 100% =

\frac{1}{5}

× 100% = 20% → (E)

Answer

Sanity check by comparing E to the rest. E = 5 students out of 25 is one-fifth, and one-fifth of 100% is 20%, which lands on (E). Also, E's bar is shorter than A and B but taller than D, so E should account for a middling slice of the class — well below A's

\frac{6}{25}

= 24% and well above D's

\frac{2}{25}

= 8%. Twenty percent sits exactly in that window. Finally, the five percentages 24, 32, 16, 8, 20 add to 100%, confirming the class total of 25 is correct.

💡Key takeaway

Read each bar, add them for the class total, then write the E-share as a fraction and turn it into a percent — a Grade 6 part-to-whole move that turns an AMC 8 problem into one step of arithmetic.

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