SHSAT Sunset

COST OF ORANGES

2022 Handbook

2022 Test A Math · Question 51 of 57

Question

COST OF ORANGES

Number of Oranges Cost
4 $1.80
6 $2.70
9 $4.05

The table shows the cost of oranges. What is the unit rate for the cost per orange?

  • A$0.45
  • B$0.90
  • C$1.35
  • D$1.80
Show the answer

Correct answer: A

The unit rate (cost per orange) can be determined by dividing the cost of x oranges by x.

1.804=2.706=4.059=0.45\frac{1.80}{4} = \frac{2.70}{6} = \frac{4.05}{9} = 0.45

The unit rate is $0.45.

Question analysis

A table shows what 4, 6 and 9 oranges cost, in dollars and cents. Students find the unit rate, the cost of a single orange. It tests identifying a unit rate in a proportional table, and the tricky part is keeping straight which column holds the cost and which holds the number of oranges.

NYS standards
  • 7.RP.2b constant of proportionality
  • 6.NS.3 multi-digit decimal operations
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Below grade 7 Finding a unit rate in a table belongs to grade 7 proportional relationships, but here it takes one division with money in a clearly proportional table, so the task is easier than typical grade 7 work.
Estimated difficulty
Routine: one familiar step, little to misread.
Solution
1 step
Reading level
Question and choices: about grade 3, 23 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

Any row gives the rate in one division, and the three rows agree, so the question is easy once unit rate is read as the cost of one orange. The traps are differences between rows, which look like a change per orange but cover two or three oranges, and the first cost in the table, which is for four. Dividing a second row confirms the result.

  1. Reading a figure, table or graph minor Understanding the question

    The table lists 4, 6 and 9 oranges but never a single orange, so the cost of one has to be computed from a row, such as $1.80 ÷ 4. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)

  2. Something you must already know minor Working it out

    The term unit rate is not defined; students must know it means the cost of one orange, a row's cost divided by its number of oranges. (Anderson & Krathwohl, 2001)

Strategy: Pick any row and divide its cost by its number of oranges; doing the same with a second row confirms that the rate stays the same.

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.
  • 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

Unit rate
unit rate=costnumber of oranges\text{unit rate} = \frac{\text{cost}}{\text{number of oranges}}
The unit rate is the cost of one item, here one orange. The cost is what a group of oranges costs together. Divide by the number of oranges in that group. Any row of the table gives the same rate, because each orange costs the same.

  1. Sort out the question

    The table gives the cost of 4, 6 and 9 oranges. It never shows the cost of one orange. A unit rate is the amount for one unit. Here that means the cost of one orange. You need to find it.

  2. Divide one row

    Use the first row: 4 oranges cost $1.80.

    unit rate=costnumber of oranges\text{unit rate} = \frac{\text{cost}}{\text{number of oranges}}

    unit rate=1.804=0.45\text{unit rate} = \frac{1.80}{4} = 0.45

    One orange costs $0.45. Watch out: $1.80 is the cost of 4 oranges, not one. Don’t pick choice D.

  3. Check with the other rows

    2.706=0.454.059=0.45\frac{2.70}{6} = 0.45 \qquad \frac{4.05}{9} = 0.45

    Every row gives $0.45, so the rate stays the same. Watch out: 2.70−1.80=0.902.70 - 1.80 = 0.90 is the cost of 2 more oranges, choice B. 4.05−2.70=1.354.05 - 2.70 = 1.35 is the cost of 3 more, choice C. Neither is for one orange. So the answer is A, $0.45.

Check your answer

Multiply back: 0.45×4=1.800.45 \times 4 = 1.80 and 0.45×9=4.050.45 \times 9 = 4.05. Both match the table. Even a difference works once you divide: 0.90÷2=0.450.90 \div 2 = 0.45.

More questions like this

The original DOE question

Question 108 as printed on page 95 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2023 Admissions, page 95, question 108. Open page 95 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).