Question

A football team sell home shirts and a The ratio of home shirts to away shirts sold is 5:1 shirts. The home shirts can either be adult's shirts of children's shirts. The ratio of adults shirts sold to children's shirts sold is 3:2 What proportion of shirts sold are children's home shirts?​

Answer 1

Explanation:

the ratio 5:1 tells us that the total amount of sold shirts can be split into 6 (5 + 1) equal parts.

5 of these 6 parts are home shirts, and 1 of these 6 parts are away shirts.

so,

5/6 of all sold shirts were home shirts.

1/6 of all sold shirts were away shirts.

the ratio 3:2 tells us that the total amount of sold home shirts can be split into 5 (3 + 2) equal parts.

3 of these 5 parts are adult shirts, and 2 of these 5 parts are children's shirts.

one part is

5/6 / 5 = 5/6 / 5/1 = 5×1 / (6×5) = 1/6

so,

3× 1/6 = 3/6 = 1/2 of all sold shirts were adults home shirts.

2× 1/6 = 2/6 = 1/3 of all sold shirts were children's home shirts.

Answer 2

Let's assume that the football team sells a total of 100 shirts.

According to the ratio given, 5/6 of the total shirts sold are home shirts, and 1/6 are away shirts.

Out of the 5/6 of home shirts, the ratio of adult's shirts sold to children's shirts sold is 3:2. So, we can divide the home shirts into two parts:

Adult's home shirts: (3/5) * (5/6) = 1/2
Children's home shirts: (2/5) * (5/6) = 1/3
Therefore, the proportion of children's home shirts sold is 1/3 of the total shirts sold, or approximately 33.33%.