Question

The women's department of a store stocks 4 types of black socks for every 5 types of white socks. The men's department stocks 6 types of black socks for every 7 types of white socks. If each department has the same number of black socks, which department stocks more types of white socks?

Answer 1

Answer:

The women's department of a store stocks have more types of  white socks.

Step-by-step explanation:

Given:

The women's department of a store stocks 4 types of black socks for every 5 types of white socks.

Ratio of black socks to white socks = 4 : 5

The men's department stocks 6 types of black socks for every 7 types of white socks.

Ratio of black socks to white socks = 6 : 7

Each department has the same number of black socks.

Question asked:

Which department stocks more types of white socks?

Solution:

Let each department has 100 black socks.

For women's department

4 : 5 : : 100 : white socks

$\frac{4}{5} =\frac{100}{White\ socks} \\\\ By \ cross \ multiplication\\ \\ 4\times White\ socks=100\times5\\ 4White\ socks=500\\By\ \ dividing\ both \ sides\ by\ 4\\White\ socks=125$

For men's department

6 : 7 : : 100 :  white socks

$\frac{6}{7} =\frac{100}{White\ socks} \\\\ By \ cross\ multiplication\\ \\ 6White\ socks=100\times7\\6White\ socks=700\\White\ socks=About\ 117$

We found that out of 100 black socks the women's department of a store stocks have 125 white socks while the men's department stocks have about 117 white socks then by default understood that the women's department of a store stocks have more types of  white socks.