Find two positive numbers

Find two positive numbers whose difference is 27 and whose product is 874.

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x = one number
y = other number

x - y = 27  {difference is 27}
xy = 874  {product is 874}

Solve the first equation for x.
x - y = 27  {first equation from above}
x = y + 27   {added y to each side of first equation}

Now substitute, for x, into second equation.
xy = 874  {second equation from above}
(y + 27)(y) = 874   {substituted (y + 2y), in for x, into second equation}
y² + 27y = 874   {used distributive property}
y² + 27y - 874 = 0   {subtracted 874 from each side}
(y + 46)(y - 19) = 0   {factored into two binomials}
y + 46 = 0  or  y - 19 = 0   {set each factor equal to zero}
y = -46   or   y = 19   {solved each equation for y}

y = 19   {only accepting positive numbers}

x = y + 27  {equation from above}
x = 19 + 27   {substituted 19, in for y, into equation from above}
x = 46   {added}

19 and 46 are the two positive numbers

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