Official Guide13 - PS Q#182 Percent

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?
A.7% loss
B.13% loss
C.7% profit
D.13% profit
E.15% profit

I think Mitch's solution using weighted averages is, by far, the best way to go here. However, if you didn't spot that approach, it's important to recognize that we really don't need to use the information about the cameras selling for $250 each. The question boils down to . . .

54 cameras were sold at a 20% markup, and cameras were sold at a 50% markdown. What was the approximate profit or loss as a percent of the dealer’s initial cost for all 60 cameras?

So, we can assign an easy value of $100 to the initial cost per camera.
This means the 60 cameras cost $6000 to buy.

54 cameras were sold at a 20% markup and 6 cameras were sold at a 50% markdown.
So, 54 cameras were sold for $120, and 6 cameras were sold for $50.
(54)($120) + (6)($50) = $6780
So, the cameras were sold for $6780

This represents a profit of $780

If the initial cost was $6000, we must determine the percentage equivalent to $780/$6000

$780/$6000 = 78/600 = 13/100 = 13%

Answer = D

Cheers,
Brent

adt29 wrote:

I think Mitch's solution using weighted averages is, by far, the best way to go here.

Brent and Mitch,
A little slow here: how do you think of weights in this problem? Are the weights the percents (20% markup and then 50% loss)? if that's the case, then according to the weighted avg formula, the denominator should be a sum of the weights right? how do you know to divide by 60?

Thanks in advance for your help!

Here's Mitch's solution:
Average for all 60 cameras = (54*20 - 6*50)/60 = 780/60 = 13

This is the same as:
Average for all 60 cameras = (54/60)20 + (6/60)(-50)
So, 54/60 of the inventory solve for a 20% profit
To this, we add the fact that 6/60 of the inventory solve for a 50% loss

I hope that helps.

Cheers,
Brent