In general, a store that sells goods to the public is called a retail store (or retailer). A retail store typically buys its merchandise directly from the manufacturer or from a wholesaler. A wholesaler is a company that buys large quantities of goods from a manufacturer and then resells the goods to retail stores. In order to make a profit, both the wholesaler and the retailer must sell their goods at a higher price than they paid for them. The difference between the cost of an item and its selling price is called the markup.
Suppose a wholesaler buys televisions for $250 each and sells them to a retail store for $300 each.
A) What is the markup?
The markup is the difference between the cost to the wholesaler ($250) and the price to the retailer ($300):
change = vnew - vold = 300 - 250 = $50 markup
B) What is the percent markup?
The wholesale percent markup is found by dividing the wholesaler's markup by the wholesaler's cost:
If change = rvold then r = change/vold = 50/250 = 0.2 = 20.0% markup
Suppose the retail store in example 1 applies a markup of 30% to determine the selling price of its televisions. What price will the retailer put on the price tag of the television that it bought from the wholesaler for $300?
change = rvold = 0.30 * 300 = $90 markup vnew = vold + change = 300 + 90 = $390 is the selling price
Sometimes, in an effort to increase sales, a retail store will discount the price of an item. When a discount is applied to a price, the price decreases. Suppose the retail store in example 2 puts the television that it normally sells for $390 on sale at 5% off.
A) What is the sale price?
change = rvold = 0.05 * 390 = $19.50 discount vnew = vold + change = 390 - 19.50 = $370.50 per television
Note that a discount of $19.50 represents a change of -$19.50 in the price.
B) What is the percent markup on the television based on the sale price?
change = vnew - vold = 370.50 - 300 = $70.50 markup
The percent markup is found by dividing the markup by the cost:
If change = rvold then r = change/vold = 70.50/300 = 0.235 = 23.5% markup
Suppose our retailer wants to sell all of the current stock of televisions before the new models arrive. The retailer advertises a clearance sale with the televisions priced at 10% off the already low sale price (from example 3).
A) What is the clearance sale price?
change = rvold = 0.10 * 370.50 = $37.05 discount vnew = vold + change = 370.50 - 37.05 = $333.45 per television
B) What is the rate of discount based on the original selling price?
change = vnew - vold = 390 - 333.45 = $56.55 discount
The discount rate is found by dividing the discount by the original price:
If change = rvold then r = change/vold = 56.55/390 = 0.145 = 14.5% discount
C) What is the retailer's markup rate based on the clearance price?
change = vnew - vold = 333.45 - 300 = $33.45 markup
The percent markup is found by dividing the markup by the cost:
If change = rvold then r = change/vold = 33.45/300 = 0.1115 = 11.15% markup
Suppose a customer buys the television at the clearance sale price ($333.45) in a state that requires 6% sales tax. What amount will appear on the customer's credit card statement?
change = rvold = 0.06 * 333.45 = $20.01 tax vnew = vold + change = 333.45 + 20.01 = $353.46
The total amount charged to the customer's credit card for this television will be $353.46.
A furniture store applies a 30% markup to the items it sells. If a sofa sells for $699.99, how much did the furniture store pay for the sofa?
vnew = vold + change = vold + rvold = vold(1 + r)
implies vold = vnew/(1 + r) = 699.99/(1 + 0.30) = 699.99/1.30 ≈ $538.45
The furniture store paid about 538.45 for the sofa.
A man who weighs 250 pounds decides to go on a diet. To keep track of his progress, he weighs himself at the end of every month and calculates the percent loss or gain compared to what he weighed at the beginning of the month. During the first month he had a 8% weight loss, during the second month he had a 5% weight loss, during the third month he had a 2% weight loss and during the fourth month he had a 2% weight gain. What was his weight after four months and what was the total percent decrease in weight?
A) What was his weight after four months?
change = rvold = 0.08 * 250 = 20 pounds vnew = vold + change = 250 - 20 = 230 pounds after 1 month change = rvold = 0.05 * 230 = 11.5 pounds vnew = vold + change = 230 - 11.5 = 218.5 pounds after 2 months change = rvold = 0.02 * 218.5 = 4.37 pounds vnew = vold + change = 218.5 - 4.37 = 214.13 pounds after 3 months change = rvold = 0.02 * 214.13 = 4.2826 pounds vnew = vold + change = 214.13 + 4.2826 = 218.4126 pounds after 4 months
B) What was the total percent decrease in weight?
change = vnew - vold = 250 - 218.4126 = 31.5874 pound weight loss
The percent change is found by dividing the change by the original weight:
If
change = rvold
then
r = change/vold = 31.5874/250 = 0.1263496 ≈ 12.63% decrease in weight