Find two positive numbers whose difference is 27 and whose product is 2680.

**x = one positive number**

y = other 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**