Original Number

[Guest]

A man purchased a set of identical pictures for $100. Five of the pictures were later damaged. The remainder were sold at a gain of $2 on the original cost of each. As a result $20 was gained on the whole transaction. Calculate original number of pictures.

[Guest]

must have sold 10 pics 2 x 10 = 20 and 5 damaged so 15total

[Guest]

if last post is right then question is wrong??

15 items bought for $100 means $6.67 average each

sold for $2 profit each sold for $8.67 each

only 10 sold total sale = $86.70

which is not $20 profit on total of transactions

[Guest]

Question is right- solution is wrong.

[Guest]

A man purchased a set of identical pictures for $100. Five of the pictures were later damaged. The remainder were sold at a gain of $2 on the original cost of each. As a result $20 was gained on the whole transaction. Calculate original number of pictures.

Let all the purchased pictures in the set be x. For all of them the man paid the total amount of $100. It means that each one's cost is [tex]\frac{100}{x }[/tex].
Five of the pictures were later damaged and respectively could not be sold. So the man had already x-5 pictures at his disposal.Each one of these pictures was sold with a profit of $2 on the original cost.
[tex]\Rightarrow (x-5).(\frac{100}{x}+2)[/tex]
This sum includes the gain of $20 on the whole transaction.
[tex]\Rightarrow (x-5).(\frac{100}{x}+2)=120 \Leftrightarrow (x-5)(100+2x)=120x[/tex]
[tex]2x^2-30x-500=0; x=25;x=-10[/tex]
The negtive x could not be a number of pictures in a set.[tex]x>0[/tex]
So the pictures were 25.

[Guest]

So 20 pics were sold at a profit $2 each giving 2 x 20 = $40 profit on the selling transaction.
5 pics damaged giving a loss of 5 x 4 = $20 loss due to damage
net profit on both transactions is 40 - 20 = $20 gain over both transactions