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Anya contributed $1,200 toward the purchase

2019 Handbook

2019 Test A Math · Question 21 of 57

Question

Anya contributed $1,200 toward the purchase of a $2,000 computer. Her brother contributed $240 toward the same computer. Her parents provided the rest of the money for the computer. What percentage of the total cost of the computer did Anya’s parents pay?

  • A24%
  • B28%
  • C32%
  • D36%
Show the answer

Correct answer: B

First, calculate the amount of money Anya’s parents contributed:

2,000−1,200−240=5602{,}000 - 1{,}200 - 240 = 560.

Then, find what percentage of $2,000 is $560:

5602,000=0.28=28%\frac{560}{2{,}000} = 0.28 = 28\%

Question analysis

Anya puts $1,200 and her brother $240 toward a $2,000 computer, and their parents pay the rest. Students find what percent of the cost the parents paid. It is a two-step percent word problem in which the percent describes an amount the stem never states.

NYS standards
Grade level
Grade 6 content, by NYS standard
Compared with grade 7
Below grade 7 Writing a part as a percent of a whole is grade 6 work. Finding the parents' share first is quick subtraction, and a total of $2,000 makes the division easy, so this is lighter than grade 7's multistep percent problems.
Estimated difficulty
Straightforward: two steps or one careful reading.
What makes it hard
Solution
2 steps
Reading level
Question and choices: about grade 8, 39 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

Two easy steps, a subtraction and a division by $2,000, make up the whole solution, so the risk lies in skipping the first. The parents' share is never stated, and a student hunting the stem for a percent finds the brother's $240, whose digits echo one of the choices. The other two wrong percents match no working with the stated amounts and catch only guesses.

  1. Turning words into math minor Understanding the question

    “Her parents provided the rest of the money” hides the amount the question is about: $2,000 − $1,200 − $240 = $560 must be found before any percent. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

Strategy: Subtract both contributions from $2,000 to find the parents' share, then divide that share by $2,000 and change the decimal to a percent.

Traps

  • Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Percent of a total
percent=partwhole×100\text{percent} = \frac{\text{part}}{\text{whole}} \times 100
The part is the amount you are asking about, here what the parents paid. The whole is the full amount, the cost of the computer. Dividing gives the fraction of the cost. Multiplying by 100 turns that fraction into a percent, a number out of 100.

  1. Sort out the question

    The computer costs $2,000. Anya paid $1,200. Her brother paid $240. Her parents paid the rest. “The rest” means whatever was still left to pay. You need the parents’ part as a percent of the whole $2,000. The question never gives the parents’ amount, so find it first.

  2. Find what the parents paid

    Take Anya’s money and her brother’s money away from the full cost.

    2,000−1,200−240=5602{,}000 - 1{,}200 - 240 = 560

    The parents paid $560.

    Watch out: the brother’s $240 has the same digits as 24%, choice A. But the question asks about the parents, not the brother.

  3. Write the parents’ share as a percent

    Use the percent formula. The part is $560, and the whole is $2,000.

    percent=partwhole×100\text{percent} = \frac{\text{part}}{\text{whole}} \times 100

    percent=5602,000×100=28100×100=28\text{percent} = \frac{560}{2{,}000} \times 100 = \frac{28}{100} \times 100 = 28

    To simplify, divide the top and the bottom of the fraction by 20. That gives 28 out of 100, which is 28%. So the answer is B, 28%.

Check your answer

Find everyone’s share. Anya paid 1,200 out of 2,000, which is 60%. Her brother paid 240 out of 2,000, which is 12%. The parents paid 28%. Together, 60+12+28=10060 + 12 + 28 = 100. The three shares make up the whole cost, so 28% fits.

More questions like this

The original DOE question

Question 78 as printed on page 100 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2019–2020, page 100, question 78. Open page 100 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).