SOLUTION: positive integer is 11 more than 28 times another. Their product is 11420. Find the two integers

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Question 964084: positive integer is 11 more than 28 times another. Their product is 11420. Find the two integers
Answer by LinnW(1048)   (Show Source): You can put this solution on YOUR website!
Set x = the larger number
y = the smaller number
x = 11 + 28y
x*y = 11420
substitute ( 11+28y ) for x
( 11+28y )y =11420
11y + 28y^2 = 11420
28y^2 + 11y - 11420 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1279161 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 20, -20.3928571428571. Here's your graph:

Based upon solver solution above, y = 20
Since x*y = 11420,
x = 11420/20
x = 571
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