The fifth graders are planning a pizza party. Each fifth grader will eat two slices of pizza with a favorite topping. One-half of the students want pepperoni. One-fourth of the students want xtra cheese. One-eighth of the students want sausage. Four students want mushrooms. How many students select a favorite topping for their pizza slices?

32 students choose a favorite topping for their slices.

Let x be the total number of students.

1/2 of the total students, or 1/2x, choose pepperoni.

1/4 of the total students, or 1/4x, choose extra cheese.

1/8 of the total students, or 1/8x, choose sausage.

4 students choose mushrooms.

We know that together, these equal the total number of students, x:

1/2x+1/4x+1/8x+4=x

We will use 8 as the common denominator:

4/8x+2/8x+1/8x+4=x

Combining like terms:

7/8x+4=x

Subtract 7/8x from both sides:

7/8x+4-7/8x=x-7/8x

4=1x-7/8x

4=1/8x

Divide both sides by 1/8:

4: (1/8) = 1/8x: (1/8)

4/1: (1/8) = x

4/1*8/1 = x

32/1 = x

32 = x