Competition · AMC preparation · step 4 of 4

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 the bar heights

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

Check the total

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 order

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

spaghetti/manicotti = 250/100

4STEP 4

Reduce the fraction

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

250/100 = (250 ÷ 50)/(100 ÷ 50) = 5/2 → (E)

Answer

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.

Read the bar heights
Check the total
Write the ratio in order
Reduce the fraction

A parent dashboard for the family lives at sensimlab.com.

Read the bar heights

Check the total

Write the ratio in order

Reduce the fraction

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