can you please help me with this word problem?

Question

Joseph sold 21 CDs at $12.25 each. For each CD sold, he made a profit of ninety-five cents. His cost has not changed, but he wants to make an average profit of $2.04. How many CDs must he sell at $17.97 each to earn an overall average profit of $2.04 per CD?
can u please help me with it? can u show the work intead of with the answer only so i can get how to do it thx :]

Answer 1

if he made a .95 profit on each, then his cost was 11.30
his profit when he sells them at 17.97 is 6.67, then
he sold 12 at .95 profit
how many at 6.67 profit does he need to sell to get the avg up to 2.04?

Answer 2

Ol' Joe sold 21 CDs for $12.25 ea.
He earned .95 on ea. one sold.
He therefore paid $11.30 ea. for them.

Average profit is:
gross profit/number sold
gross profit is sale price - cost * number sold

You have to figure out how much total profit Jie has to earn selling the at $17.97 each to average an overall profit of $2.04

His original gross profit was 21*.95=19.95
His new sales will equal X*6.67=6.67X
His total gross profit will be
21*.95+ X*6.67/(21+X)=2.04
19.95+6.67X/(21+X)=2.04
19.95+6.67X=43.84+2.04X
4.63X = 23.89
X=~5

Answer 3

Average=(Total Profit)/(Number Sold)

You want an average profit of 2.04. We should find out how much each CD costs him by subtracting .95 from 12.25. This is 11.3. He is buying CDs for $11.30. If he wants to sell CDs at $17.95 each, he will earn $6.65 per CD.

Set up an equation.

2.04=((.95*21)+(6.65*n))/(n+21)

n=number of CDs sold at new price.

Simplify the above and you will get n=4.97 CDs, or round to 5


I hope that this helps

Answer 4

let him sell x C.D.s @17.97 average out $2.04 profit
total sale proceeds=17.97x+21(12.25+0.95)
the equation (x+21)(12.25+2.04)
=17.97x+21(12.25+0.95)
solvefor x