On the Ford Aquatics swim team, 11 year olds and 12 year olds swim together. The Gold team has a 2:3 ratio of 11 year olds to 12 year olds. The Silver team has a 3:8 ratio of 11 year olds to the total swimmers. If the two teams have the same number of 11 year olds what could the size of the teams be?

Respuesta :

Answer:

The Gold team has 8 swimmers and the silver team also has 8 swimmers.

Step-by-step explanation:

Let T be the total number of swimmers on the Gold team. Since, the Gold team has a 2:3 ratio of 11 year olds to 12 year olds, the number of 11 year old is T' = 2/(2 + 3) × T = 2T/5 and the number of 12 year olds is T" = 3/(2 + 3) × T = 3T/5.

The silver team has a 3:8 ratio of 11 year olds to the total swimmers. Let T₁ be the number of 11 year old swimmers in the silver team. So, from the ratio 3:8, the number of 11 year old swimmers in the silver team is 3 and the total number of swimmers in the silver team is 8.

Since the number of 11 year old swimmers in both teams are the same, then

2T/5 = 3

T = 3 × 5 ÷ 2

T = 15/2

T = 7.5

T≅ 8

So, the Gold team also has 8 swimmers.

So, the Gold team has 8 swimmers and the silver team also has 8 swimmers.