The product of two numbers is 24 find the numbers if one number is two more than twice the other.

Let the numbers be x and
y

Given that the product is
24.

==> x*y =
24.............(1)

Now we know that one number is 2 more
than twice the other number.

==> x = 2y+ 2
..............(2)

We will substitute (2) into
(1).

==> (2y+2)*y =
24

==> 2y^2 + 2y =
24

We will divide by
2.

==> y^2 + y=
12

==> y^2 +y - 12 =
0

==> (y+4)(y-3) =
0

==> y1= -4  ==>  x1= 2*-4+2 =
-6

==> y2= 3  ==> x2= 2*3+2 =
8

Then we have two sets of
solution.

==> The numbers are 3 and
8   OR   -4 and -6.