Question

Angie bought 500 identical dresses for $12 500.

She sold 350 dresses at a marked price of 30% above the cost price.
Each of the remaining dresses was sold at half the marked price.
Express Angie's profit as a percentage of her cost price.​

Answer 1

10.5%

Explanation:

The fraction Angie sold at 130% of the cost price was 350/500 = 0.7. The remaining 0.3 of the dresses were sold at 130%/2 = 65% of the cost price.

Angie's net on the deal was ...

(0.7)(130%) +(0.3)(65%) = 91% +19.5% = 110.5%

where 100% is Angie's cost price. Her profit is this percentage less 100%.

Angie's profit as a percentage of her cost price was 10.5%.

_____

Alternate solution

Obviously, you can work out the cost price of each dress ($25) and the marked up price ($32.50). Then you can work out the revenue for 350 dresses ($11,375) and the revenue from the sale of the remaining 150 dresses at half price ($16.25 × 150 = $2,437.50). Angie's total revenue ($13,812.50) less the cost price is her profit ($1,312.50). Divided by her original cost, this will be her profit: $1,312.50/$12,500 × 100% = 10.5%.