Answer
The two numbers are 19 and 36.
Work Step by Step
x + y =55
We know that the sum of these two unknown numbers is 55, so we set up an equation that states that one unknown number (x) plus another unknown number (y) equals 55.
x $\times$ y = 684
We also know that the product of these two unknown numbers is 684. So we set up another equation that states this.
We will use one of these equations to isolate one unknown number in order to substitute into the other equation. We will use the equation x + y = 55.
x + y = 55
y = 55-x We isolate y by itself by subtracting x from both sides.
Now we have y on one side by itself.
We now take the other equation, x $\times$ y = 684, and substitute 55 - x for y.
We then get:
x (55 - x) = 684
55x - $x^{2}$ = 684 We use the FOIL method to distribute terms.
55x - $x^{2}$ - 684 = 0 We subtract 684 from each side to make the
equation equal to zero.
$x^{2}$ - 55x + 684 = 0 We divide each side by -1.
(x - 19) (x - 36) = 0 We factor this equation.
x - 19 = 0 Now we can set each product equal to zero by
x - 36 = 0 using the zero product property.
x = 19 We add 19 to each side.
x = 36 We add 36 to each side.
The two numbers that we are looking for are 19 and 36.
