# college math

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one number is 8 more than twice another. their product is 8 more than twice their sum. find the numbers

• college math -

N1=8+2*N2
N1*N2=8+2(N1+N2)

• college math -

Let the smaller number be x; that means the other number must be 2x + 8.

Solve the equation
x(2x+8) = 2x + 8 + x + 8

which can also be written

2x^2 + 8x = 3x + 16
or
2x^2 + 5x -16 = 0

There seems to be no integer solution. The smaller number is
x = (-5 + sqrt 153)/4 = 1.84233
and the larger number is 2x + 1 = 11.68466
Their sum is 13.5267
and the product is 21.527
as required.

• college math -

drwls, you made a slight mistake - you forgot a factor of 2 in the RHS of the equation.

If N1 = x and N2 = 2x + 8
then the equation is
x(2x+8) = 8 + 2*(2x + 8 + x)
Which simplifies to
x^2 - x - 12 = 0
which has two integer solutions.

Hope that helps!

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