A pet store sells mice in 2 colors: brown and white. If 3/5 of the mice are brown, the ratio of male mice to female mice is 2:1, and 1/2 of the female mice are white, then what is the ratio of the number of brown male mice to the number of white male mice?

Question

A pet store sells mice in 2 colors: brown and white. If 3/5 of the mice are brown, the ratio of male mice to female mice is 2:1, and 1/2 of the female mice are white, then what is the ratio of the number of brown male mice to the number of white male mice?

Answer 1

1/3 of the mice are female, so

1/6 of the mice are white female
1/6 of the mice are brown female

3/5 are brown, so 3/5-1/6 = 13/30 are white male

1-(1/3+13/30) = 7/30 are brown male

So, brownmale/whitemale = 7/13

Answer 2

To find the ratio of the number of brown male mice to the number of white male mice, we need to gather the necessary information and follow these steps:

Step 1: Determine the proportion of brown mice to white mice. We are given that 3/5 of the mice are brown, so we can calculate the proportion of white mice as 1 - 3/5 = 2/5.

Step 2: Calculate the proportion of female mice. The ratio of male mice to female mice is given to be 2:1, meaning there are 2 parts males for every 1 part female. To determine the proportion of females, we can divide 1 by the sum of the ratio parts, which is 2 + 1 = 3. Therefore, the proportion of female mice is 1/3.

Step 3: Calculate the proportion of white female mice. We are given that half of the female mice are white, so we can calculate the proportion of white females as 1/2 multiplied by 1/3 = 1/6.

Step 4: Calculate the proportion of white male mice. Since we know the proportion of white mice is 2/5 and the proportion of white female mice is 1/6, we can infer that the proportion of white male mice is the difference between these two values: 2/5 - 1/6 = 7/30.

Step 5: Calculate the proportion of brown male mice. Since we know the proportion of male mice to female mice is 2:1, and the total proportion of males is 3 parts (2 for brown and 1 for white), we can deduce that the proportion of brown males is 2/3 multiplied by the proportion of brown mice, which is 3/5. This equals (2/3) * (3/5) = 6/15.

Step 6: Calculate the ratio of brown male mice to white male mice. To find the ratio, divide the proportions of brown males by the proportions of white males: (6/15) / (7/30).

Simplifying the division, we get: (6/15) * (30/7) = 36/21.

Therefore, the ratio of brown male mice to white male mice is 36:21, which can be reduced to 12:7.