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.