social arithmetic

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Social ArithmeticSocial Arithmetic

Selling Price, Mark-ups Selling Price, Mark-ups Markdowns, Discount, Markdowns, Discount,

Commission, Sales Tax, Commission, Sales Tax, Profit & Simple InterestProfit & Simple Interest

TOPIC 9TOPIC 9

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Terminology

Selling Price - The price retailers charge customers

Cost - The price retailers pay to a manufacturer

Markup, margin, or gross profit - The difference between the cost of bringing the goods into the store and the selling

price

Operating expenses or overhead - The regular

expenses of doing business such as rent, wages,

utilities, etc.

Net profit or net income - The profit remaining after subtracting the cost of bringing the goods into the

store and the operating expenses

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Basic Selling Price Formula

Selling price (S) = Cost (C) + Markup (M)

$1,200Computer

$900 - Pricepaid to bring

computerinto store

$300 - Dollars to

cover expenses and

profit

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Calculating Dollar Markup and Percent Markup on Cost

• Johnny buys Sunday’s newspaper for $1.00. He plans to sell them for $1.50. What is Johnny’s markup? What is his percent markup on cost?

Dollar Markup = Selling Price - Cost

$ .50 = $1.50 - $1.00

Percent Markup on Cost = Dollar Markup Cost$.50 = 50%$1.00

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Calculating Selling Price When You Know Cost and Percent Markup on Cost

• Ray’s Appliances bought a refrigerator for $150. To make desired profit, he needs a 60% markup on cost. What is Ray’s dollar markup? What is his selling price?

S = C + MS = $150 + .60($150)S = $150 + $90S = $240 Dollar Markup

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Calculating Cost When You Know Selling Price and Percent Markup on Cost

• Jane’s imported flower business sells floral arrangements for $35. To make her desired profit, Jane needs a 40% markup on cost. What do the flower arrangements cost Jane? What is the dollar markup?

S = C + M$35 = C + .40(C)$35 = 1.40C1.40 1.40$25 = C

M = S - CM = $35 - $25 M = $10

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Markdowns

Carrefour marked down a $50 tool set to $36. What are the dollar

markdown and the markdown percent?

$36

$14$50

28%

$50-$36Markdown

Markdown percent = Dollar markdown Selling price (original)

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DISCOUNT

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Discount is the difference between the regular price and the sale price of an item. You can use percent of decrease to find discounts.

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Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the discounted price?

Example 1: Finding Discount

(450)(0.20) = 90 Find 20% of $450. This is the amount of discount.

450 – 90 = 360 Subtract $90 from $450.

Multiply, then subtract.

The discounted price was $360.

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Example 2: Finding Discount

(85)(0.40) = 34 Find 40% of $85. This is the amount of markup.

85 + 34 = 119 Add $34 to $85.

Multiply, then add.

Mr. Olsen has a computer business in which he sells everything 40% above the wholesale price. If he purchased a printer for $85 wholesale, what will be the retail price?

The retail price is $119.

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Check It Out! Example 3A

(750)(0.10)= 75 Find 10% of $750. This is the amount of discount.

750 – 75 = 675 Subtract $75 from $750.

Multiply, then subtract.

Lily bought a dog house originally priced at $750 that was on sale for 10% off. What was the sale price?

The sale price was $675.

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COMMISSION

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A commission is a fee paid to a person who makes a sale. It is usually a percent of the selling price. This percent is called the commission rate.

commission ratecommission rate salessales = commissioncommission

Commission

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A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month?

Multiplying by Percents to Find

Commission Amounts

First find his commission.

4% $65,000 = c commission rate sales = commission

0.04 65,000 = c Change the percentto a decimal.

2600 = c Solve for c.

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Example 1 Continued

He earned a commission of $2600 on the sale.Now find his total pay for last month.

$2600 + $900 = $3500 commission + salary = total pay.

His total pay for last month was $3500.

A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month?

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A car sales agent is paid a monthly salary of $700 plus commission. Last month she sold one sports car for $50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month?

Check It Out! Example 1

First find her commission.

5% $50,000 = c commission rate sales = commission

0.05 50,000 = c Change the percent to a decimal.

2500 = c Solve for c.

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Check It Out! Example 1 Continued

The agent earned a commission of $2500 on the sale.

Now find her total pay for last month.

$2500 + $700 = $3200 commission + salary = total pay.

Her total pay for last month was $3200.

A car sales agent is paid a monthly salary of $700 plus commission. Last month she sold one sports car for $50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month?

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SALES TAX

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Sales tax is the tax on the sale of an item or service. It is a percent of the purchase price and is collected by the seller.

Sales Tax

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If the sales tax rate is 6.75%, how much tax would Adrian pay if he bought two CDs at $16.99 each and one DVD for $36.29?

Example : Multiplying by Percents to Find Sales Tax Amounts

CD: 2 at $16.99 $33.98

DVD: 1 at $36.29 $36.29

$70.27 Total Price

0.0675 70.27 = 4.743225 Write the tax rate as a decimal and multiply by the total price.

Adrian would pay $4.74 in sales tax.

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Amy reserves a hotel room for $45 per night. She stays for two nights and pays a sales tax of 13%. How much tax did she pay?

$45 2 = $90 Find the total price for the hotel stay.

$90 0.13 = $11.70 Write the tax rate as a decimal and multiply by the total price.

Amy spent $11.70 on sales tax.

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Profit

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A furniture store earns 30% profit on all sales. If total sales are $2790, what is the profit?

Example 3A: Finding Profit

and Total Sales

Think: What is 30% of 2790?

x = 0.30 2790 Set up an equation.

x = 837

The profit is $837.

Multiply.

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Think: 10,044 is 30% of what number?

Let s = total sales

10,044 = 0.30 s Set up an equation.

33,480 = s Simplify.

The total sales are $33,480.

A furniture store earns 30% profit on all sales. If the store earns $10,044, how much are the total sales?

Example 3B: Finding Profit

and Total Sales

10,044 0.30

= Divide each side by 0.30. 0.30s 0.30

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A retail store earns 40% profit on all sales. If total sales are $3320, what is the profit?

Check It Out! Example 4A

Think: What is 40% of 3320?

x = 0.40 3320 Set up an equation.

x = 1328

The profit is $1328.

Multiply.

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Think: 5,680 is 40% of what number?

Let s = total sales

5,680 = 0.40 s Set up an equation.

14,200 = s Simplify.

The total sales are $14,200.

A furniture store earns 40% profit on all sales. If the store earns $5,680, how much are the total sales?

Check It Out! Example 4B

5,680 0.40

= Divide each side by 0.04. 0.40s 0.40

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SIMPLE INTEREST

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When you deposit money into a bank, the bank pays you interest.

When you borrow money from a bank, you pay interest to the bank.

I = P r t

Simple interest is money paid only on the principal.

Principal is the amount of money borrowed or invested.

Rate of interest is the percent charged or earned.

Time that the money is borrowed or invested (in years).

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To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?

Additional Example 1: Finding Interest and Total Payment on a Loan

First, find the interest she will pay.

I = P r t Use the formula.

I = 15,000 0.09 3 Substitute. Use 0.09 for 9%.

I = 4050 Solve for I.

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Additional Example 1 Continued

Jessica will pay $4050 in interest.

P + I = A principal + interest = total amount

15,000 + 4050 = A Substitute.

19,050 = A Solve for A.

You can find the total amount A to be repaid on a loan by adding the principal P to the interest I.

Jessica will repay a total of $19,050 on her loan.

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To buy a laptop computer, Elaine borrowed $2,000 for 3 years at an annual simple interest rate of 5%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?


First, find the interest she will pay.


I = 2,000 0.05 3 Substitute. Use 0.05 for 5%.


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Elaine will pay $300 in interest.

P + I = A principal + interest = total amount

2000 + 300 = A Substitute.

2300 = A Solve for A.

You can find the total amount A to be repaid on a loan by adding the principal P to the interest I.

Elaine will repay a total of $2300 on her loan.

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Additional Example 2: Determining the Amount of Investment Time


450 = 6000 0.03 t Substitute values into the equation.

2.5 = t Solve for t.

Nancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested?

450 = 180t

The money was invested for 2.5 years, or 2 years and 6 months.

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200 = 4000 0.02 t Substitute values into the equation.

2.5 = t Solve for t.

TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested?

200 = 80t

The money was invested for 2.5 years, or 2 years and 6 months.

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I = 1000 0.0325 18 Substitute. Use 0.0325 for 3.25%.


The interest is $585. Now you can find the total.

Additional Example 3: Computing Total Savings

John’s parents deposited $1000 into a savings account as a college fund when he was born. How much will John have in this account after 18 years at a yearly simple interest rate of 3.25%?

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P + I = A Use the formula.



John will have $1585 in the account after 18 years.


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I = 1000 0.075 50 Substitute. Use 0.075 for 7.5%.


The interest is $3750. Now you can find the total.


Bertha deposited $1000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%?

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Bertha will have $4750 in the account after 50 years.


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Mr. Johnson borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money?

Additional Example 4: Finding the Rate of Interest


8000 + I = 10,320 Substitute.

I = 10,320 – 8000 = 2320 Subtract 8000 from both sides.

He paid $2320 in interest. Use the amount of interest to find the interest rate.

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2320 = 32,000 r Simplify.


2320 = 8000 r 4 Substitute.

232032,000

= r Divide both sides by 32,000.

0.0725 = r

Mr. Johnson borrowed the money at an annual rate

of 7.25%, or 7 %.14

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Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money?



9000 + I = 20,000 Substitute.

I = 20,000 – 9000 = 11,000 Subtract 9000 from both sides.

He paid $11,000 in interest. Use the amount of interest to find the interest rate.

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11,000 = 90,000 r Simplify.


11,000 = 9000 r 10 Substitute.

11,000 90,000

= r Divide both sides by 90,000.

0.12 = r

Mr. Mogi borrowed the money at an annual rate of about 12.2%.

social arithmetic

Business

commission commission

price cost

price s

percent markup

cost c

c commission rate sales

dollar markup cost

price retailers