Find two positive numbers whose difference is 21 and whose product is 1150.
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. Ask Algebra House
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