Question 1102005: The Music Store paid $14.95 for a DVD. Expenses are 21% of regular selling price and the required profit is 11% of regular selling price. During an inventory sale, the DVD was marked down 20%.
(a) What was the regular selling price?
(b) What was the sale price?
(c) What was the operating profit or loss
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! cost of the DVD is 14.95
operating expense is 21% of the regular selling price.
required profit is 11% of the regular selling price.
total operating cost is cost of the DVD plus operating expense.
this is equal to 14.95 + .21 * the regular selling price.
required profit is equal to regular selling price minus total operating cost
this translates to:
.11 * regular selling price = regular selling price minus .21 * regular selling price minus 14.95
add 14.95 to both sides of this equation and subtract .11 * regular selling price from both sides of this equation to get:
14.95 = regular selling price minus .21 * regular selling price minus .11 * regular selling price.
factor out regular selling price to get:
14.95 = regular selling price * (1 - .21 - .11)
combine like terms to get:
14.95 = regular selling price * .68
solve for regular selling price to get regular selling price = 14.95 / .68.
this results in regular selling price = 21.98529412
from the regular selling price, you can now calculate expense and required profit.
you get:
expense is equal to .21 * regular selling price = 4.616911765
required profit is equal to .11 * regular selling price = 2.418382353
discount is equal to 20% of the regular selling price = 4.397058824.
discounted selling price is equal to regular selling price minus discount = 17.58823529
your total cost is equal to the cost of the DVD plus the expense.
this is equal to 14.95 + 4.616911765 = 19.56691176
everything seems to check out.
your total cost is equal to 19.56691176
your regular selling price is 21.98529412
your required regular profit is equal to regular selling price minus your total cost = 2.418382353 which is equal to .11 * your regular selling price.
your discounted sale price is equal to .8 * your regular selling price = 17.58823529
your profit based on the discounted sale price is equal to 17.58823529 - 19.56691176 = -1.978676471
a negative profit is equal to a loss, therefore you have a loss of 1.978676471.
based on all of this, your solution is:
(a) the regular selling price was 21.98529412 = 21.99
(b) the sale price was 17.58823529 = 17.59
(c) the operating loss was 1.978676471 = 1.98
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