Simple word problem causes dispute

Question

A company purchases 200 VCR units at a price of \$220 each. For each order of 200, there is a fee of \$25 added as well.

If the company sells each VCR unit at a price marked up 30 percent, what is the profit per unit?

-First dispute was that no one buys VCRs anymore. Agreed! Let's look past this point . . .

Some students solved by doing the following; 200 units costs \$220 each with a \$25 fee, so:

200 * 220 + 25
44000 + 25
44025

That's the cost. Now the revenue, a 30% mark up of the cost price, times the number of units, so:

(1.3 * 220) * 200
286 * 200
57200

That's the total revenue. The total profit is the difference:

57200 - 44025
13175

And divide by the number of units to get the profit per unit:

13175 / 200 = \$65.88 per unit (rounded to nearest penny)

Others solved this way; Calculate the cost per unit as 220.125 - Because of the \$25 fee added. So, \$44025 / 200 = 220.125
220.125 * 1.3 = \$286.1625
\$286.1625 - \$220.125 = \$66.0375
To nearest penny, I calculate a profit of \$66.04

What is the true profit per unit?

Answer 1

This dispute is if the order fee applies per order or per VCR, and it seems from the wording that the per order fee must apply per order, not per VCR, so the second approach is correct.

Answer 2

The dispute on the profit per VCR is $ 66.04-65.88=.16.$

This is the result of charging the customers for the ordering fee of $25(1.3)=32.5$ dollars in the second case.

Note that the total extra charge of $32.54$ divided into $200$ unites is $.1625$ per unit.

Both cases make sense depending on who pays the ordering fee.

Answer 3

The word "added" implies the buyer (the company) pays the fee.

The confusion is with the word "a price (marked up)": is it a list (sticker, nominal) price or a real price that the company paid per unit.

The formula of a unit profit is: $$\frac{\pi}{Q}=\frac{TR-TC}{Q}=\frac{P^*Q-(PQ+fee)}{Q}.$$ As long as it is agreed upon what the selling price $P^*$ is, calculating the top (numerator, profit) first and then dividing by $Q$ will be the same as dividing the terms by $Q$ first and then subtracting.