The product of two numbers is 800. The difference between the numbers is 20. What are the two numbers?
x = one number
y = the other number xy = 800 {the product of two numbers is 800} x  y = 20 {their difference is 20} Solve the second equation for x, by adding y to each side. x  y = 20 {the second equation} x = y + 20 {added y to each side} Substitute (y + 20), in for x, into first equation. xy = 800 {first equation} (y + 20)y = 800 {substituted (y + 20) in for x} y² + 20y = 800 {used distributive property} y² + 20y  800 = 0 {subtracted 800 from each side} (y + 40)(y  20) = 0 {factored into two binomials} y + 40 = 0 or y  20 = 0 {set each factor equal to zero} y = 40 or y = 20 {solved each equation for y} Substitute 40 and 20, back in for y, into first equation. If y = 40 xy = 800 {first equation} 40x = 800 {substituted 40 for y} x = 20 {divided each side by 40} The product of 20(40) = 800 The difference of 20  (40) = 20 + 40 = 20 {this could be argued, based on the negatives} If y = 20 xy = 800 {first equation} 20x = 800 {substituted 20 in for y} x = 40 {divided each side by 20} The product of 20(40) = 800 the difference of 40  20 = 20 x = 40 and y = 20 or x = 20 and y = 40 Pfew! Ask Algebra House
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