If 36/y=4x , what is the value of x when y=3 ?

If 36/y = 4x, what is x when y = 3

2018 Handbook

2018 Test B Math · Question 20 of 57

Also in 2026 Practice Test B Math, question 18; 2025 Practice Test B Math, question 20.

Question

If $\frac{36}{y}=4x$ , what is the value of $x$ when $y=3$ ?

Show the answer

Correct answer: A

Substitute 3 for $y$ and solve for $x$ :

$\frac{36}{y}=4x$

$\frac{36}{3}=4x$

$12=4x$

$3=x$

Question analysis

This equation question gives 36 divided by y equal to 4x and asks for the value of x at one given value of y. Students substitute, simplify the fraction and solve a one-step equation. It is short, so the risk lies in stopping one step early or dividing by the wrong number.

NYS standards: 6.EE.7 one-step equations
6.EE.2c evaluating expressions and order of operations
Grade level: Grade 6 content, by NYS standard
Compared with grade 7: Below grade 7 Substituting a value and solving a one-step equation are grade 6 skills. With two quick steps and whole numbers, this is lighter than the multistep equations typical of grade 7.
Estimated difficulty: Routine: one familiar step, little to misread.
Thinking it demands: Depth of knowledge 1, recall and reproduction · mainly apply
What makes it hard: Variables instead of numbers minor
Solution: 2 steps
Reading level: Question and choices: about grade 8, 10 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

This is substitution followed by a one-step equation, with small whole numbers throughout, so most students answer correctly. The only real risk is stopping at 12, which is the value of 4x rather than of x. Writing 12 = 4x as its own line before reading the choices makes the last division hard to skip.

Variables instead of numbers minor Understanding the question
The variable y sits in a denominator, 36/y, which looks less familiar than an equation in one unknown, though substituting y = 3 removes it at once. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

Strategy: Replace y with its value, simplify the left side to a single number, and then divide by the coefficient of x.

Traps

Stops one step early: A choice is a number from partway through the solution.

The wrong answers, classified

B Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: weak
Picks the coefficient 4 from 4x, a number that appears in the equation, without solving for x.
C Stops one step early (King et al., 2004; Gierl et al., 2017)
Reveals partial knowledge Expected pull: moderate
Clears the fraction to get 36 = 4xy, divides by 4 to reach xy = 9, and stops before dividing by y.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Reveals partial knowledge Expected pull: strong
Substitutes y = 3 to get 36/3 = 12, which is the value of 4x, and stops before dividing by 4.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Undoing multiplication: $a \times x = b \text{ means } x = b \div a$; a is the number multiplied by x, and b is the result. Division undoes multiplication. So to get x alone, divide both sides by a.

Write down what you know
The equation is $\frac{36}{y} = 4x$ . You are told y = 3. You need the value of x.
The letter y is on the bottom of a fraction. Putting in its value turns the fraction into a plain number.
Put in the value of y
Replace y with 3.
$\frac{36}{3} = 4x$
The fraction means 36 divided by 3, which is 12.
$12 = 4x$
Watch out: 12 is the value of 4x, not x. Stopping here gives choice D.
Divide both sides by 4
4x means 4 times x. To undo multiplying by 4, divide both sides by 4.
$x = 12 \div 4 = 3$
So the answer is A, 3.

Check your answer

Put x = 3 and y = 3 back in. The left side is $36 \div 3 = 12$ . The right side is $4 \times 3 = 12$ . Both sides match, so x = 3 is right.

The original DOE question

Question 77 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 77. Open page 157 of the handbook (PDF)