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