The ratio of the number of adults to the number of children at a concert is 5 to 3. If there is a total of 120 people at the concert, how many are children?

Question

The ratio of the number of adults to the number of children at a concert is 5 to 3. If there is a total of 120 people at the concert, how many are children?

Answer 1

Hi Brianna, the ratio 5 to 3 tells us for every 8 people, 5 will be adults and 3 will be children. Let x represent the number of children at the concert. Set up a proportion representing the given information:

3 / 8 = x / 120

Cross multiply:

8x = 3 * 120, or 360

Divide by 8

x = 45

There were 45 children at the concert.

The number of adults at the concert is 120 - 45, or 75.

The ratio of adults to children, 75 / 45. Dividing both the numerator and denominator by 15 gives: 5 / 3.

Questions?

Answer 2

We can find this by setting two fractions equal to one another that represent part/whole and in this case #kids/total and solve for x:

3/8 = x/120

360 = 8x

45 = x

There are 45 children.