Question 140326
The difference between two positive numbers is 4. If twice the square of the larger number is added to three times the smaller the sum is 53. Solve.
:
you were on the right track, however, you can just use x as the variable:
:
Let x = a number
then
(x-4) = the smaller number 
:
Write the equation like you did without using y
: 
2x^2 + 3(x-4) = 53
:
2x^2 + 3x - 12 = 53; Multiply what's inside the brackets
:
2x^2 + 3x - 12 - 53 = 0
:
2x^2 + 3x - 65 = 0
Factor
(2x+13)(x-5) = 0
:
2x = -13
x = -6.5
and
x = +5
;
:
It says the numbers have to be positive:
5, 1 are the numbers
:
I'll let you check out these solutions in the original equation