AMC 8 · 2003 · #3

Grade 6 rate-ratio

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

percentagefraction-arithmeticcomplementary-counting identify-subproblemscomplementary-counting ↑ Prerequisites: fraction-decimal-conversionmulti-digit-arithmetic

📏 Short solution 💡 2 insights

Problem

A burger at Ricky C's weighs 120 grams total, and 30 grams of that is filler. What percent of the burger is not filler?

Pick an answer.

(A)

$60\%$

(B)

$65\%$

(C)

$70\%$

(D)

$75\%$

(E)

$90\%$

AMC 8 2003 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Set Up an Equation

The question asks for a percent, which is a part-over-whole equation. Tool #3 (Set Up an Equation) gives the formula directly: percent = (non-filler weight) ÷ (total weight) × 100%. The trap is reading the problem too fast and computing the filler percent ( $\frac{30}{120}$ = 25%) instead of the non-filler percent. Tool #9 (Solve an Easier Problem) handles that by first finding the non-filler weight as its own sub-problem, then plugging it into the percent equation.

1STEP 1

Subtract the filler from the total to get the non-filler weight: 90 grams.

non-filler = 120 - 30 = 90 grams

2STEP 2

Put the non-filler over the whole burger in the percent formula: $\frac{90}{120}$ .

percent =

\frac{part}{whole}

× 100% =

\frac{90}{120}

× 100%

3STEP 3

Reduce by dividing top and bottom by 30: $\frac{3}{4}$ .

\frac{90}{120}

\frac{3}{4}

4STEP 4

Convert $\frac{3}{4}$ to a percent and match the choice.

\frac{3}{4}

× 100% = 75% → (D)

Answer

75%

Cross-check by computing the filler percent instead:

\frac{30}{120}

\frac{1}{4}

= 25%. Filler + non-filler must total 100%, and 25% + 75% = 100%. The numbers also pass a feel test — only one-quarter of the burger is filler, so three-quarters is the real thing, which lands on (D). Choice (E) 90% is the trap that comes from reading 90 grams as a percent directly; (A) 60% and (C) 70% are common "round number" distractors that ignore the actual ratio.

💡Key takeaway

Percent questions ask "part out of the whole" — pin down which weight is the part, simplify the fraction, then read off the percent.

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