Rates predict

Question

90 out 120 like to work out and 5 out of every 18 of those who like to work out have a gym membership. At the same rates in a group of 216 predict how many you would expect to have a gym membership.

Answer 1

90  out of 120 like to work out means that 3/4 of a group like to work out.

 

5 out of every 18 who like to work out have a gym membership, then 5/18 have a gym membership who like to workout.  Since 3/4 like to work out, (3/4) * (5/18) = 5/24 of the 120, or (5/24) * 120 = 25 of the original 120 have a gym membership.

 

In a group of 216 people, (5/24) * 216 = 45 would have a gym membership.

 

This can be verified also as follows, if 90 out of 120 like to work out then let x of 216 be the number who like to work out:   90/100 = 3/4 = x/216.

From this 162 out of 216 people would like to work out.

 

Also, 5/18 of those who like to work out have a gym membership, (5/18) * 162 = 45 who would have a gym membership.

 

Finally also, if 25 out of 120 have a gym membership, let y be number of 216 who have gym membership.

Then 25/120 = y/216 => y = (25/120) * 216 = 45

 

Like many problems, there are several different approaches that can be used to find answers.