Find two positive numbers

​Find two positive numbers whose difference is 21 and whose product is 1150.

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x = one number
y = other number

x - y = 21 {difference is 21}
xy = 1150 {product is 1150}

Solve first equation for x, and then substitute into other equation.

x - y = 21 {first equation}
x = y + 21 {solved first equation for x}

xy = 1150 {second equation}
(y + 21)y = 1150 {substituted (y + 21), in for x, into second equation}
y² + 21y = 1150 {used distributive property}
y² + 21y - 1150 = 0 {subtracted 1150 from each side}
(y + 46)(y - 25) = 0 {factored into two binomials}
y + 46 = 0 or y - 25 = 0 {set each factor equal to 0}
y = -46 or y = 25 {solved each equation for y}

y = 25 {only positive numbers for answers}

Substitute 25, in for y, into x - y = 21.

x - 25 = 21 {substituted 25, in for y}
x = 46 {added 25 to each side}

46 and 25 are the two numbers.

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