Find the two numbers given their difference and their product

Find two positive numbers whose difference is 27 and whose product is 2680.
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x = one positive number 
y = other positive number 

x - y = 27    {their difference is 27}
xy = 2680    {their product is 2680}

x - y = 27    {the first equation}
x = y + 27    {added y to each side}

xy = 2680    {the second equation}
(y + 27)y = 2680    {substituted (y + 27), in for x, into second equation}
y² + 27y = 2680      {used the distributive property}
y² + 27y - 2680 = 0    {subtracted 2680 from each side}
(y + 67)(y - 40) = 0    {factored  into two binomials}
y + 67 = 0   or   y - 40 = 0    {set each factor equal to zero}
y = -67   or   y = 40    {solved each equation for x}

Using only the positive number, 40.

x = y + 27   {first equation, re-arranged}
x = 40 + 27   {substituted 40, in for y, into (y + 27)}
x = 67   {added}

40 and 67 are the two numbers 

- Algebra House
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