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.
This is what I have
x - y = 4
2x squared + 3y = 53
This is where I got lost.
Thank you
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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