Question 200483: 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. please help. thank you
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two positive numbers; x, y
;
Write an equation for each statement:
:
"the difference between two positive numbers is 4."
x - y = 4
-y = -x + 4
Multiply by -1;
y = (x - 4); use for substitution
:
"If twice the square of the larger number is added to three times the smaller, the sum is 53."
2x^2 + 3y = 53
:
Replace y with (x-4) in the above equation
2x^2 + 3(x-4) = 53
:
2x^2 + 3x - 12 - 53 = 0
Arrange as a quadratic equation:
2x^2 + 3x - 65 = 0
Factor
(2x + 13)(x - 5) = 0
Two solutions
2x = -13
x = -6.5,
and
x = +5; then y = 1; assume they want the integer solution
:
:
Check solution
2(5^2) + 3(1) = 53
:
:
The other solution: x=-6.5, y=-10.5, will also satisfy the equation
2(-6.5^2) + 3(-10.5) =
2(42.25) - 31.5 =
84.5 - 31.5 = 53
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