Question 1153731

let {{{x}}} be the number of ${{{1}}} discounts

then price of each book is {{{20-x}}}

a bookstore currently sells {{{15}}} copies, and with a discount, the store can sell {{{3}}} more books: {{{3x}}}
so, the number of books sold is {{{15+3x}}}

then

{{{(20-x)(15+3x)=468}}}
{{{300+60x-15x-3x^2=468}}}
{{{300+45x-3x^2-468=0}}}
{{{-3x^2+45x-168=0}}}...factor
{{{-3 (x^2-15x+56) =0}}}
{{{-3 (x^2-8x-7x+56) =0}}}
{{{-3 ((x^2-8x)-(7x-56)) =0}}}
{{{-3 (x(x-8)+7(x-8)) =0}}}
{{{-3(x-8)(x-7)=0}}}

solutions:
{{{x=8}}}
or
{{{x=7}}}

the number of ${{{1}}} discounts that will yield sales of ${{{468}}} per week is: {{{7}}} and {{{8}}}