Nicole’s age now is three times

2018 Handbook

2018 Test B Math · Question 27 of 57

Also in 2026 Practice Test B Math, question 23; 2025 Practice Test B Math, question 27.

Question

Nicole’s age now is three times Carmen’s age. If Carmen will be 17 in two years, how old was Nicole 5 years ago?

A38 yr
B40 yr
C45 yr
D50 yr

Show the answer

Correct answer: B

First, find out how old Nicole and Carmen are now.

Let $N$ = Nicole’s age now. Let $C$ = Carmen’s age now.

$C+2=17$

$C=15$ (Carmen’s age now)

$N=3C$

$N=3(15)=45$ (Nicole’s age now)

$N-5=45-5=40$ (Nicole’s age 5 years ago)

Question analysis

This age word problem says Nicole is three times as old as Carmen now, and that Carmen will be 17 in two years. Students work out both present ages and then go back five years for Nicole. Keeping the times straight is the tricky part: two years ahead for Carmen, five years back for Nicole.

NYS standards: 7.EE.4 equations and inequalities from problems
6.EE.7 one-step equations
Grade level: Grade 7 content, by NYS standard
Compared with grade 7: At grade 7 Grade 7 students write simple equations from word problems. Age problems like this one take three short steps, and the shifts in time are the only real hurdle, so the demand is typical of grade 7.
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: Turning words into math moderate
Much to keep track of minor
Solution: 3 steps
Reading level: Question and choices: about grade 1, 25 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 arithmetic is short, but the question moves through three points in time, and only one of them carries the three-times relationship. Students who find Nicole's present age often stop there, since it is a choice. Labeling each age with its time, now or then, keeps the two-year and five-year shifts with the right person and in the right direction.

Turning words into math moderate Understanding the question
Three points in time appear, now, in two years and 5 years ago, and “three times Carmen's age” holds only for now, so each shift must be applied to the right person. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Much to keep track of minor Working it out
Students must hold Carmen's future age 17, her present age 15, Nicole's present age 45 and the 5-year shift while deciding which to report. (Sweller, 1988; Carpenter, Just & Shell, 1990)

Strategy: Find Carmen's age now by going back two years from 17, triple it for Nicole's current age, then subtract five.

Traps

Stops one step early: A choice is a number from partway through the solution.
Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)

The wrong answers, classified

A Misreads the question (Hegarty, Mayer & Monk, 1995)
Reveals a slip Expected pull: weak
Applies the two-year shift to Nicole as well, subtracting both 2 and 5 from her present age of 45.
C Stops one step early (King et al., 2004; Gierl et al., 2017)
Reveals partial knowledge Expected pull: strong
Finds Nicole's present age, three times 15, and stops before going back 5 years.
D Negatives and direction (Brown & Burton, 1978)
Reveals a slip Expected pull: moderate
Adds 5 years to Nicole's present age instead of subtracting, giving her age 5 years from now.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Age at another time: $\text{age in } n \text{ years} = \text{age now} + n$; n is a number of years. To find an age in the future, add n to the age now. To find an age in the past, subtract n instead. Everyone gets older at the same speed, one year per year.

Sort out the times
The question talks about three times: now, two years from now, and 5 years ago. Nicole is 3 times as old as Carmen now.
Carmen will be 17 in two years. You need Nicole’s age 5 years ago.
Find Carmen's age now
In two years Carmen will be 17. So right now she is 2 years younger.
$17 - 2 = 15$
Carmen is 15 now.
Find Nicole's age now
Nicole’s age now is three times Carmen’s age now.
$3 \times 15 = 45$
Nicole is 45 now.
Watch out: 45 is her age now, choice C. The question asks about 5 years ago.
Go back 5 years
Going back in time means subtracting.
$45 - 5 = 40$
Nicole was 40 five years ago.
Watch out: Adding 5 gives 50, choice D. Also, the 2 years only apply to Carmen. Taking 2 more years off Nicole gives 38, choice A.
So the answer is B, 40 yr.

Check your answer

Work forward from your answer. Nicole was 40 five years ago, so she is 45 now. Carmen is a third of that, 15. In two years Carmen will be 17. That matches the question.

The original DOE question

Question 84 as printed on page 158 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 158, question 84. Open page 158 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).