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

Step-by-step 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

Answer 2

Answer:$\frac{1}{3}$

Step-by-step explanation:

Given

There are $\frac{5}{7}$  as many barrettes as hair ties in Sasha's hair supplies

i.e. $\frac{Barrettes}{hair ties}=\frac{5}{7}$

Hair ties =$Barrettes\frac{7}{5}$

Also There $\frac{5}{8}$barrettes  as hair bands in Sasha's supplies

i.e. $\frac{Barrettes}{hair bands}=\frac{5}{8}$

Hair Bands=$Barrettes\frac{8}{5}$

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

$\frac{Barrettes}{Hair band +ties}=\frac{Barrettes}{Barrettes\frac{8}{5}+Barrettes\frac{7}{5}}$

$=\frac{1}{\frac{8}{5}+\frac{7}{5}}=\frac{5}{8+7}$

$=\frac{5}{15}=\frac{1}{3}$