Question

Some girls in a Girl Scout troop are pairing up with some boys in a Boy Scout troop to practice square dancing. Two-thirds of the girls are paired with three-fifths of the boys. What fraction of the scouts are square dancing?

(Each pair is one Girl Scout and one Boy Scout. The pairs are only from these two troops.)

Answer 1

Fraction of the scouts are square dancing is
`(19)/(30)`.

Explanation:

Each pair is one Girl Scout and one Boy Scout.

So, to the final fraction ( of the pairs) we are going to get 1/2 from the fraction of girls and 1/2 from the fraction of boys.

Girls=
`(2)/(3) *(1)/(2) =(2)/(6)`

Boys=
`(3)/(5) *(1)/(2) =(3)/(10)`

To get the fraction of the scouts that are square dancing, we have to add the fraction of girls , with the fraction of boys.

=
`(2)/(6) +(3)/(10)`

=
`((2*10) +(6*3))/(6*10) =\\ (20+18)/(60)`

=
`(38)/(60)`

=
`(19)/(30)`

This means that from 30 scouts , 19 are dancing.