# 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

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Let us assume that he larger number is y

and the smaller number is x

The larger is 5/2 the smaller:

==> y= (5/2)x.....(1)

Also :

2y-2x 12 .....(2)

Now substitute with y= (5/2)x

==> 2(5/2)x -2x =12

==? 5x-2x= 12

==> 3x= 12

==> x= 4

==> y= (5/2)x= (5/2)*4= 10

Let us say that the larger number is x and the smaller is y. That gives us the following equations.

x = 2.5y

2x - 2y = 12

5y - 2y = 12

3y = 12

y = 4

So now we plug that value for y into the first equation.

x = 2.5(4)

That gives us

x = 10

We can also check this by using the second equation. We set it up like this:

2x - 2y = 12

2*10 - 2*4 = 12

20 - 8 = 12

Since this is correct, we have found the correct values for x and y.

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.