Question

The ratio of athletes in the two teams is 3:2. After 12 athletes move from first team to second, the ratio is 5:4. Find the number of athletes on each team originally.

Answer 1

x is the number of athletes on first team originally ( x > 12, x ∈ Nˣ )

y ----------------------------------------second------------------( y ∈ Nˣ )

The ratio of athletes in the two teams is 3:2

⇒
`(x)/(y) =(3)/(2)` (1)

After 12 athletes move from first team to second, the ratio is 5:4

⇒
`(x-12)/(y+12) =(5)/(4)` (2)

(1),(2) ⇒
`\left \{ {{(x)/(y) =(3)/(2)} \atop {(x-12)/(y+12) =(5)/(4)} \right. <=>\left \{ {{x=162} \atop {y=108}} \right.`

So: The first team originally has 162 numbers and the second team originally has 108 numbers

ok done. Thank to me :>

Answer 2

Explanation:

Let the athletes be 3x and 2x.

Now, By the question we get,

(3x-12)/(2x+12) = 5/4

or, 12x-48= 10x+60

or, 2x = 108

so, x = 54

now

3x= 3×54= 162

2x = 2×54=108

The number of athletes were 162 in first team and 108 in second team originally.