Find two positive numbers whose difference is 27 and whose product is 2680.
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, rearranged} x = 40 + 27 {substituted 40, in for y, into (y + 27)} x = 67 {added} 40 and 67 are the two numbers Ask Algebra House Comments are closed.

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