A United States presidential coin

2018 Handbook

2018 Test B Math · Question 24 of 57

Also in 2026 Practice Test B Math, question 22; 2025 Practice Test B Math, question 24.

Question

A United States presidential coin is made from an alloy of four metals—copper, zinc, manganese, and nickel—with weights in the ratio of $177:12:7:4$ , respectively. The coin weighs a total of 8 grams. What is the weight of the zinc in this coin?

A0.28 g
B0.48 g
C0.96 g
D48 g

Show the answer

Correct answer: B

Add the four values in the ratio

(177 + 12 + 7 + 4 = 200)

and use the sum as the denominator. Use that to find the fraction of zinc in one of the coins. Then reduce the fraction:

$\frac{12}{200}=\frac{3}{50}$

Multiply this fraction by 8 to find the number of grams of zinc in decimal form:

$\frac{3}{50}\times 8=\frac{24}{50}=0.48\text{ g}$

Question analysis

This ratio word problem describes a United States presidential coin made of four metals in the ratio 177:12:7:4 by weight, and asks how many grams of zinc are in an 8-gram coin. Students turn a part-to-whole ratio into a fraction and multiply. Matching each metal to its number and handling the decimal result need care.

NYS standards: 7.RP.3 multistep ratio and percent problems
Grade level: Grade 7 content, by NYS standard
Compared with grade 7: At grade 7 Using a part-to-whole ratio to split a total is ratio work grade 7 students practice often. The four-term ratio and a decimal answer add a little care, but the demand matches typical grade 7 work.
Estimated difficulty: Straightforward: two steps or one careful reading.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: Hard words minor
Error-prone arithmetic minor
Solution: 3 steps
Reading level: Question and choices: about grade 3, 47 words.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The method, adding the parts and taking zinc's share of the total, is standard, and the parts conveniently add to 200. Students lose points by picking the wrong term of the four-part ratio or by assuming the parts are out of 100. The last check is size: no part of an 8-gram coin can weigh 48 grams.

Hard words minor Understanding the question
Construct-irrelevant reading: the words “alloy” and “respectively” carry the setup, and only “respectively” tells students that zinc is the second term, 12, of 177:12:7:4. (Perfetti, 2007; Freedle & Kostin, 1993)
Error-prone arithmetic minor Working it out
Taking 12 parts out of 200 of an 8-gram coin produces 96/200, a decimal under one gram, where a misplaced point gives 4.8 or 48. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

Strategy: Add the four ratio numbers to get the total parts, write zinc's share as a fraction of that total, and multiply by the coin's 8 grams.

Traps

Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.

The wrong answers, classified

A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Reveals a slip Expected pull: moderate
Uses manganese's 7 parts instead of zinc's 12, misreading which term goes with which metal, and gets 7/200 × 8 = 0.28.
C Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Reveals a misconception Expected pull: moderate
Treats zinc's 12 parts as 12 percent, dividing by 100 instead of the 200 total parts, so finds 0.12 × 8 = 0.96.
D An arithmetic slip (Junker & Sijtsma, 2001)
Reveals a slip Expected pull: weak
Loses the decimal point, multiplying 8 by 6 instead of 0.06, though no part can outweigh the 8-gram coin.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Share of a ratio: $\text{part} = \frac{\text{its ratio number}}{\text{sum of the ratio numbers}} \times \text{total}$; The ratio numbers tell how many equal shares each metal gets. Their sum is the number of shares in the whole coin. One metal's fraction is its shares over all the shares. Multiply by the total weight to get that metal's weight.

Match each metal to its number
The ratio is 177:12:7:4. “Respectively” means in the same order as the list of metals. So copper is 177, zinc is 12, manganese is 7 and nickel is 4.
The whole coin weighs 8 grams. You need the weight of the zinc.
Watch out: Using manganese’s 7 instead of 12 gives 0.28 g, choice A.
Count the total parts
$177 + 12 + 7 + 4 = 200$
The coin is made of 200 equal parts by weight. Zinc has 12 of those parts.
Find zinc's fraction
Zinc’s fraction is its ratio number over the sum of the ratio numbers.
$\frac{12}{200} = \frac{12 \div 4}{200 \div 4} = \frac{3}{50}$
Zinc is $\frac{3}{50}$ of the coin’s weight.
Watch out: Do not divide by 100. The ratio adds to 200, not 100. Treating zinc as 12% gives 0.96 g, choice C.
Multiply by the coin's weight
Multiply zinc’s fraction by the weight of the whole coin, 8 grams.
$\text{part} = \frac{3}{50} \times 8 = \frac{24}{50} = \frac{48}{100} = 0.48$
The zinc weighs 0.48 grams.
So the answer is B, 0.48 g.

Check your answer

Zinc is a small share, 12 out of 200, so it must weigh well under 1 gram. 0.48 g fits. Choice D, 48 g, is heavier than the whole 8-gram coin, so it cannot be right.

The original DOE question

Question 81 as printed on page 157 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 157, question 81. Open page 157 of the handbook (PDF)