Question

A sporting goods store sells 90 jackets for $200 dollars each. Each $10 decrease in price would result in 5 more jackets sold. How do you find the number of jackets sold and the selling price to give revenues of $17600 from jacket sales?

Answer 1

To earn `$176000` cost price and number of sale should be`($160 and 110) or ($220 and 80)`

Explanation:

Let the number of decrease of `$10` in cost be `x`

Then, new reduced cost price is `$(200- 10 x)` and

increased sale of jackets is `(90+5 x)`

Revenues earned is `(200-10 x) (90+5 x)= 17600` or

`-50 x^2 +100 x +18000=17600` or

`50x^2 -100 x =400 or x^2 -2 x -8=0` or

`(x-4)(x+2)=0 :. x= 4 , x=-2`

when `x=4` , the price of jackets be `200-10*4= $160`

and number of sells of jacket is `90+5*4=110` and revenue

earned is `110*160=$17600`.

when `x=-2` , the price of jackets be `200-10*(-2)= $220`

and number of sells of jacket is `90+5*(-2)=80` and revenue

earned is `80*220=$17600`.

To earn `$176000` cost price and number of sale should be

`$160 and 110 or $220 and 80` [Ans]