Question

On Wednesday, 1/3 of the students in Mr. Short's homeroom had drama practice, and 1/4 of his other homeroom students had band practice. If 6 students had band practice, how many students are in Mr. Short's homeroom?

Answer 1

36

Explanation:

Let n be the total number of students in Mr. Short's homeroom. Then, working backward, we see that

6 = 1/4(1 - 1/3)n = 1/4(2/3)n = 1/6n,$

so n = 6 x 6 = 36 students.

Answer 2

36

Explanation:

Honestly, I'd work this out visually (see image) by drawing a rectangle and dividing it up. But if you need to show the math, here's how to do it:

Let x = the number of students in the homeroom

1/3 x have drama

1/4 (x - 1/3x) have band, and we are told 6 students have band, so

1/4 (x - 1/3 x) = 6

1/4 (2/3 x) = 6

2/12 x = 6

1/6 x = 6

6 × 1/6 x = 6 × 6

1 x = 6 × 6

x = 36