Question

Two thirds of the employees at an office stated that they preferred soft cookies over crispy cookies. More than 36 employees stated their preference. Ren was asked to write, solve, and graph an inequality to find the number of employees working at the office. His work is shown below.

Step
Ren’s work

Step 1

Two-thirds x less-than 36

Step 2

x less-than 54

Step 3
A number line going from 51 to 57. An open circle is at 54. Everything to the left of the circle is shaded.


Where, if any, did Ren first make a mistake in his work?
Step 1
Step 2
Step 3
No mistake found

Answer 1

Step 1.

"More than 36" means (2/3)x > 36, not (2/3)x < 36. Correctly solving gives x > 54, so the graph should have an open circle at 54 with shading to the right.