AMC 8 · 2007 · #2

Grade 6 rate-ratio

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

ratio-proportiongraph-readingfraction-arithmetic identify-subproblems ↑ Prerequisites: graph-readingfraction-arithmetic

📏 Short solution 💡 2 insights 📊 Diagram

Problem

A bar graph shows how 650 students voted on four pasta types: lasagna, manicotti, ravioli, and spaghetti. Find the ratio of students who preferred spaghetti to students who preferred manicotti.

Pick an answer.

(A)

$$\frac{2}{5}$$

(B)

$$\frac{1}{2}$$

(C)

$$\frac{5}{4}$$

(D)

$$\frac{5}{3}$$

(E)

$$\frac{5}{2}$$

AMC 8 2007 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Visualize / Read the Picture

The whole problem lives inside the picture, so Tool #15 (Visualize) is primary — read each bar's top against the labeled gridline. Tool #2 (List Out) helps you write down the four bar heights cleanly so you do not confuse spaghetti with manicotti. Once both numbers are on the page, the ratio is a simple fraction to reduce.

1STEP 1

Read each bar against the labeled gridlines; the two we need are Spaghetti = 250 and Manicotti = 100.

Lasagna = 150, Manicotti = 100, Ravioli = 150, Spaghetti = 250

2STEP 2

Sanity check: the four heights add to 650, matching the stated total, so we read the bars right.

150 + 100 + 150 + 250 = 650 ✓

3STEP 3

Write the ratio in the asked order — spaghetti over manicotti — as the fraction $\frac{250}{100}$ .

spaghetti/manicotti =

\frac{250}{100}

4STEP 4

Both 250 and 100 divide by 50, so the fraction reduces to $\frac{5}{2}$ .

\frac{250}{100}

\frac{250 ÷ 50}{100 ÷ 50}

\frac{5}{2}

→ (E)

Answer

\frac{5}{2}

Spaghetti's bar (250) is taller than manicotti's bar (100), so the ratio must be greater than 1. That immediately rules out (A)

\frac{2}{5}

and (B)

\frac{1}{2}

. Also, the spaghetti bar is 2.5 times the manicotti bar by eye — exactly

\frac{5}{2}

. The answer (E) matches.

💡Key takeaway

Read the two bars you need, write the ratio in the order asked, then reduce the fraction. The picture does most of the work.

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