Question

the sum of two numbers is 23 and their products is 132. find the two numbers.

Answer 1

Let the two numbers be x and y, then... 1) {{{x+y = 23}}} "the sum of two numbers is 23.." 2) {{{x*y = 132}}} "...their product is 132." Rewrite equation 1) as: {{{x = 23-y}}} and substitute this for x into equation 2). 2a) {{{(23-y)*Y = 132}}} Solve for y. 2a) {{{23y-y^2 = 132}}} Rearrange into standard quadratic form. 2a) {{{y^2-23y+132 = 0}}} Factor. 2a) {{{(y-12)(y-11) = 0}}} Apply the zero product rule. {{{y-12 = 0}}} or {{{y-11 = 0}}} which means that: {{{y = 12}}} or {{{y = 11}}} The two numbers are 11 and 12.