Question

At 12pm there are 855 people in the zoo. By 5pm ⁴/₅ of the children have left and ³/₄ of the adults have left. There are now 36 more children than adults in the zoo. How many adults were in the zoo at 12pm?

Answer 1

300

Explanation:

Let x represent the number of adults in the zoo at 12 pm. Then the number of children at that time is 855 -x.

The number of remaining children is 1/5 of the number at 12 pm, so is ...

(855 -x)/5

The number of remaining adults is 1/4 of the number at 12 pm, so is ...

x/4

There are 36 more remaining children, so we have ...

(855 -x)/5 -x/4 = 36

171 -9x/20 = 36 . . . . . collect terms

135 = 9x/20 . . . . . . . . add (9/20)x-36

(20/9)(135) = x = 300 . . . . . multiply by 20/9

There were 300 adults in the zoo at 12 pm.