SOLUTION: the product of two numbers is 84. One number is 13 more than 2 times the other. Find both numbers

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Question 610698: the product of two numbers is 84. One number is 13 more than 2 times the other. Find both numbers
Answer by Maths68(1474)   (Show Source): You can put this solution on YOUR website!
Let x and y be the two numbers

The product of two numbers is 84.
xy=84.........(1)
One number is 13 more than 2 times the other.
x=2y+13..............(2)
Substitute the value of x in (1)
(2y+13)y=84
2y^2+13y=84
2y^2+13y-84=0
Solve for y
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=841 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4, -10.5. Here's your graph:

So
y=4 or y=-10.5(inadmissible)
Put the value of y=4 in (1)
xy=84
4x=84
x=84/4
x=21
x,y = 21,4

Check
======
xy=84
21*4=84
84=84

x=2y+13
21=2(4)+13
21=8+13
21=21
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