The fifth graders are planning a pizza party. Each fifth grader will eat two slices of pizza with a favorite topping. Each fifth
grader selects a favorite topping. One-half of the students want pepperoni. One-fourth of the students want extra cheese. One-eighth of the students want sausage. Four students want mushrooms. How many students select a favorite topping for their pizza slice.
There are 32 students that select a favorite topping.
Let x be the total number of students. 1/2 of the students, or 1/2x, choose pepperoni. 1/4 of the students, or 1/4x, choose cheese. 1/8 of the students, or 1/8x, choose sausage. 4 students choose mushrooms.
We know that if we add all of the students together we will get the total number of students, which we defined as x:
1/2x+1/4x+1/8x+4=x
We will use 8 as the common denominator of these fractions: 4/8x+2/8x+1/8x+4=x
Adding 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
