Question

There are 5/7 as many barrettes as hair ties in Sasha's hair supplies. There are 5/8 barrettes as hair bands in her supplies. What is the ratio of the number of barrettes to the total number of hair ties and bands?

Answer 1

Answer:
`(1)/(3)`

Explanation:

Given

There are
`(5)/(7)` as many barrettes as hair ties in Sasha's hair supplies

i.e.
`(Barrettes)/(hair ties)=(5)/(7)`

Hair ties =
`Barrettes(7)/(5)`

Also There
`(5)/(8)`barrettes as hair bands in Sasha's supplies

i.e.
`(Barrettes)/(hair bands)=(5)/(8)`

Hair Bands=
`Barrettes(8)/(5)`

Ratio of the number of Barrettes to the total number of hair ties and bands

`(Barrettes)/(Hair band +ties)=(Barrettes)/(Barrettes(8)/(5)+Barrettes(7)/(5))`

`=(1)/((8)/(5)+(7)/(5))=(5)/(8+7)`

`=(5)/(15)=(1)/(3)`

Answer 2

1/3

Explanation:

We are given ...

barrettes : hair ties = 5 : 7

barrettes : hair bands = 5 : 8

Then the combined ratios are ...

barrettes : hair ties : hair bands = 5 : 7 : 8

For every 5 barrettes, there are 7+8 = 15 hair ties and bands, so their ratio is ...

barrettes/(hair ties and bands) = 5/15 = 1/3