Question

Among the eighth-graders in Michael's school, 70% have siblings. The eighth-grade class is 5/6 the size of the seventh-grade class.
If 112 eighth-graders have siblings, how many students are in the seventh grade?

A. 128

B. 134

C. 160

D. 192

Answer 1

Answer:

D. 192

Step-by-step explanation:

This problem involves a few steps.  First, you need to determine how many eighth graders you have given that 112 represent 70% of the total number of eighth graders.  You can solve this using a proportion:

$\frac{70}{100}=\frac{112}{x}$

Cross-multiply and divide:  70x = 11200 or 70x/70 = 11200/70 or x = 160

Since there are 160 total eighth graders and this is $\frac{5}{6}$ of the amount of seventh graders, we can set up an equation to solve for the total amount of seventh graders:

160 =  $\frac{5}{6}$x

Multiply by the reciprocal of your fraction on both sides:

$\frac{6}{5}$ x 160 =  $\frac{5}{6}$x ($\frac{6}{5}$)

Solve for x:  x = 192 seventh graders