Question 819991
Let x - one number and y = the other. Then:
x + y = 94
x*y = 360<br>
We will use the Substitution Method to solve. Solving the first equation for y we get:
y = -x + 94
Substituting for y in the other equation:
x*(-x+94) = 360
Now we solve this. First we simplify:
{{{-x^2+94x = 360}}}
Since this is a quadratic equation we want one side to be zero. Since I also like a positive coefficient in fromt of {{{x^2}}} I'll add {{{x^2}}} and subtract 94x:
{{{0 = x^2-94x+360}}}
Next we factor:
0 = (x-90)(x-4)
Zero Product Property:
x-90 = 0 or x-4 = 0
Solving these:
x = 90 or x = 4<br>
Finding y (using y = -x + 94):
For x = 90: y = -(90) + 94 = 4
For x = 4: y = -(4) + 94 = 90<br>
So the two numbers are 4 and 90.