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Solve Sales Tax ApplicationsSales tax and commissions are applications of percent in our everyday lives. To solve these applications, we will follow the same strategy we used in the section on decimal operations. We show it again here for easy reference. HOW TO: Solve an application
Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it. Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item. See Figure \(\PageIndex{1}\). The sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays. Figure \(\PageIndex{1}\) - The sales tax is calculated as a percent of the purchase price. Definition: sales taxThe sales tax is a percent of the purchase price. Sales Tax = Tax Rate • Purchase Price Total Cost = Purchase Price + Sales Tax Example \(\PageIndex{1}\):Cathy bought a bicycle in Washington, where the sales tax rate was 6.5% of the purchase price. What was (a) the sales tax and (b) the total cost of a bicycle if the purchase price of the bicycle was $392? Solution (a)
(b)
Exercise \(\PageIndex{1}\):Find (a) the sales tax and (b) the total cost: Alexandra bought a television set for $724 in Boston, where the sales tax rate was 6.25% of the purchase price. Answer a$45.25 Answer b$769.25 Exercise \(\PageIndex{2}\):Find (a) the sales tax and (b) the total cost: Kim bought a winter coat for $250 in St. Louis, where the sales tax rate was 8.2% of the purchase price. Answer a$20.50 Answer b$270.50Example \(\PageIndex{2}\):Evelyn bought a new smartphone for $499 plus tax. She was surprised when she got the receipt and saw that the tax was $42.42. What was the sales tax rate for this purchase? Solution
Exercise \(\PageIndex{3}\):Diego bought a new car for $26,525. He was surprised that the dealer then added $2,387.25. What was the sales tax rate for this purchase? Answer9%Exercise \(\PageIndex{4}\):What is the sales tax rate if a $7,594 purchase will have $569.55 of sales tax added to it? Answer7.5%Solve Commission ApplicationsSales people often receive a commission, or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the rate of commission. Definition: commissionA commission is a percentage of total sales as determined by the rate of commission. commission = rate of commission • total sales To find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal. Example \(\PageIndex{3}\):Helene is a realtor. She receives 3% commission when she sells a house. How much commission will she receive for selling a house that costs $260,000? Solution
Exercise \(\PageIndex{5}\):Bob is a travel agent. He receives 7% commission when he books a cruise for a customer. How much commission will he receive for booking a $3,900 cruise? Answer$273Exercise \(\PageIndex{6}\):Fernando receives 18% commission when he makes a computer sale. How much commission will he receive for selling a computer for $2,190? Answer$394.20Example \(\PageIndex{4}\):Rikki earned $87 commission when she sold a $1,450 stove. What rate of commission did she get? Solution
Exercise \(\PageIndex{7}\):Homer received $1,140 commission when he sold a car for $28,500. What rate of commission did he get? Answer4%Exercise \(\PageIndex{8}\):Bernice earned $451 commission when she sold an $8,200 living room set. What rate of commission did she get? Answer5.5%Solve Discount ApplicationsApplications of discount are very common in retail settings Figure 6.8. When you buy an item on sale, the original price of the item has been reduced by some dollar amount. The discount rate, usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount, we multiply the discount rate by the original price. We summarize the discount model in the box below. Figure 6.8 - Applications of discounts are common in everyday life. (credit: Charleston's TheDigitel, Flickr) Definition: discountAn amount of discount is a percent off the original price. amount of discount = discount rate • original price sale price = original price − discount The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price. Example \(\PageIndex{5}\):Jason bought a pair of sunglasses that were on sale for $10 off. The original price of the sunglasses was $39. What was the sale price of the sunglasses? Solution
Exercise \(\PageIndex{9}\):Marta bought a dishwasher that was on sale for $75 off. The original price of the dishwasher was $525. What was the sale price of the dishwasher? Answer$450Exercise \(\PageIndex{10}\):Orlando bought a pair of shoes that was on sale for $30 off. The original price of the shoes was $112. What was the sale price of the shoes? Answer$82In Example 6.29, the amount of discount was a set amount, $10. In Example 6.30 the discount is given as a percent of the original price. Example \(\PageIndex{6}\):Elise bought a dress that was discounted 35% off of the original price of $140. What was (a) the amount of discount and (b) the sale price of the dress? Solution (a) Before beginning, you may find it helpful to organize the information in a list. Original price = $140, Discount rate = 35%, Amount of discount = ?
(b) Original price = $140, Amount of discount = $49, Sale price = ?
Exercise \(\PageIndex{11}\):Find (a) the amount of discount and (b) the sale price: Sergio bought a belt that was discounted 40% from an original price of $29. Answer a$11.60 Answer b$17.40 Exercise \(\PageIndex{12}\):Find (a) the amount of discount and (b) the sale price: Oscar bought a barbecue grill that was discounted 65% from an original price of $395. Answer a$256.75 $138.25 There may be times when you buy something on sale and want to know the discount rate. The next example will show this case. Example \(\PageIndex{7}\):Jeannette bought a swimsuit at a sale price of $13.95. The original price of the swimsuit was $31. Find the (a) amount of discount and (b) discount rate. Solution (a) Before beginning, you may find it helpful to organize the information in a list. Original price = $31, Amount of discount = ?, Sale price = $13.95
(b) Before beginning, you may find it helpful to organize the information in a list. Original price = $31, Amount of discount = $17.05, Discount rate = ?
Exercise \(\PageIndex{13}\):Find (a) the amount of discount and (b) the discount rate: Lena bought a kitchen table at the sale price of $375.20. The original price of the table was $560. Answer a$184.80 Answer b33% Exercise \(\PageIndex{14}\):Find (a) the amount of discount and (b) the discount rate: Nick bought a multi-room air conditioner at a sale price of $340. The original price of the air conditioner was $400. Answer a$60 Answer b15% Solve Mark-up ApplicationsApplications of mark-up are very common in retail settings. The price a retailer pays for an item is called the wholesale price. The retailer then adds a mark-up to the wholesale price to get the list price, the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the mark-up rate. To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below. Definition: mark-upThe mark-up is the amount added to the wholesale price. amount of mark-up = mark-up rate • wholesale price list price = wholesale price + mark up The list price should always be more than the wholesale price. Example \(\PageIndex{8}\):Adam's art gallery bought a photograph at the wholesale price of $250. Adam marked the price up 40%. Find the (a) amount of mark-up and (b) the list price of the photograph. Solution (a)
(b)
Exercise \(\PageIndex{15}\):Jim's music store bought a guitar at wholesale price $1,200. Jim marked the price up 50%. Find the (a) amount of mark-up and (b) the list price. Answer a600% Answer b$1,800 Exercise \(\PageIndex{16}\):The Auto Resale Store bought Pablo's Toyota for $8,500. They marked the price up 35%. Find the (a) amount of mark-up and (b) the list price. Answer a$2,975 Answer b$11,475 Practice Makes PerfectSolve Sales Tax ApplicationsIn the following exercises, find (a) the sales tax and (b) the total cost.
In the following exercises, find the sales tax rate.
Solve Commission ApplicationsIn the following exercises, find the commission.
In the following exercises, find the rate of commission.
Solve Discount ApplicationsIn the following exercises, find the sale price.
In the following exercises, find (a) the amount of discount and (b) the sale price.
In the following exercises, find (a) the amount of discount and (b) the discount rate. (Round to the nearest tenth of a percent if needed.)
Solve Mark-up ApplicationsIn the following exercises, find (a) the amount of the mark-up and (b) the list price.
Everyday Math
Writing Exercises
Self Check(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. (b) What does this checklist tell you about your mastery of this section? What steps will you take to improve? Contributors and Attributions
What pricing concept is used if all costs are considered and a fair markup is added to determine the selling price?The idea behind cost-plus pricing is straightforward. The seller calculates all costs, fixed and variable, that have been or will be incurred in manufacturing the product, and then applies a markup percentage to these costs to estimate the asking price.
In which of the following pricing methods is the markup added to manufacturing cost and selling and expenses to determine the selling price?Cost plus pricing involves adding a markup to the cost of goods and services to arrive at a selling price. Under this approach, you add together the direct material cost, direct labor cost, and overhead costs for a product, and add to it a markup percentage in order to derive the price of the product.
What cost concept used in applying the costIn using the total cost concept of applying the cost-plus approach to product pricing, selling expenses, administrative expenses, and profit are covered in the markup. The product cost concept includes all manufacturing costs in the cost amount to which the markup is added to determine product price.
When using the product cost concept of applying the costTerms in this set (12)
In using the VARIABLE COST CONCEPT of applying the cost-plus approach to product pricing, what is included in the MARKUP? Total fixed manufacturing costs, total fixed selling and administrative expenses, and desired profit.
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