The larger of two integers is 5/2 the smaller.if twice the smaller is subtracted from twice the larger, the difference is 12. Find the numbers

If twice the smaller is subtracted from twice the larger we get 12.

So the larger is half of (12+twice smaller) = smaller+6

So we assume  the smaller one is x and the larger is  x+6

 Again by the first condition the larger , x+6 is 5/2 times the smaller x. So we set up the equation x+6 = x*(5/2) =5x/2

x+6=5x/2.

2(x+6) =2* 5x/2

2x+12 = 5x

2x+12 -2x = 5x-2x

12= 3x,

12/3 =3x/3

4=x.

So the larger = 5x/2 = 5*4/2 = 10.

Therefore, larger and smaller numbers :  10 and 4.