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.

Step-by-step 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.

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

⇒      [tex]\frac{x}{y} =\frac{3}{2}[/tex]              (1)

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

⇒      [tex]\frac{x-12}{y+12} =\frac{5}{4}[/tex]         (2)

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

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

ok done. Thank to me :>

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