Percent Applications

Unit

Pre-AlgebraUnit 7B

Here are some percent frameworks that will be helpful for you!

I = PRT

Retail price = Wholesale price + Markup

is %

of 100

part %

whole 100

amount of change percent of change

original amount 100

Discounts, Coupons and SalesSometimes stores have coupons or sales that discount the price of the products they sell. The discount is usually a percentage of the original price.

Terms you may see for discounted items are: 50% off Save 50% Discounted by 50%

The discount is the amount of money you save and is subtracted from the original price.

The sale price is the new price of the item after the discount has been deducted.

For example, a $460 lawn mower is on sale for 35% off.

To find the amount of the discount, you need to calculate 35% of 460.

REMEMBER: change percents to decimals and “of” means multiply. 0.35 x 460 = 161. amount of the discount.

To find the sale price, subtract the amount of the discount from the original price. $460 – $161 = $299.

The lawn mower costs $299 on sale.

1. A $25 watch is on sale for 20% off.

Amount of discount? ________

Sale price? ____________

2. The original price of a CD player is $29.95. It is on sale for 25% off. How much do you save? What is the sale price?

4. THINKER! Dennis has a coupon for 20% off the cost of a new printer. The sale price (not including tax) is $160.00. What was the original price of the printer before the discount?

3. Sandi wants to buy some new patio furniture. A table costs $178.00. Chairs cost $63.00 each. If she bought the table and four chairs for 40% off, how much would she spend?

Sales Tax

A state sales tax is collected for most sales. Although not all states have a sales tax, the majority do. This money is used by the state for such things as education, police protection, and keeping the highways in good condition. To compute a sales tax is to find a percentage. REMEMBER, change percent to a decimal and “of” means multiply. Tax is ADDED to a purchase.

NOTE! If, when you calculate the tax, the tax is “beyond money,” the government rounds up a penny … ALWAYS!

1. You want to buy a pair of shoes that cost $85.00. There is a 7.5% sales tax. Find the amount of tax and the total price.

3. THINKER! Erik spent $22.47 on a shirt. This price includes 7% sales tax. What was the cost of the shirt without the tax?

2. Bill bought a notebook for $5.85. There was a sales tax of 5%. What was the price of the notebook with tax?

Commission

Sales commissions are paid to employees or companies that sell merchandise in stores or by calling on customers. The commission is meant to motivate sales persons to sell more. A commission may be paid in addition to a salary or instead of a salary. (In a nut shell: the more you sell, the more money you make!)

A commission is generally a percentage of the sales price of an item. For example, if a salesperson receives a 10% commission on their sales and sells $1500 worth of merchandise, they would earn (10% of 1500) $150 in commissions. REMEMBER: change percents to decimals and “of” means multiply.

1. A car salesperson earns a 6.5% commission on every car sold. The salesperson sells a car for $21,800. What is the commission?

3. The Multi Shoe Company pays its employees a salary plus 9% commission on everything they sell. Last month the top selling employee sold $18,000 worth of shoes. How much was his commission?

2. A real estate salesperson earns a 6% commission on every property they sell. What is their commission on a $128,000 home?

Leaving a Tip in a Restaurant

When you eat in a restaurant, you are expected to leave some money as a tip for the person who served your food. The tip is usually a percent of the total bill. Tips are usually about between 15% and 20% of the total bill.

If the service is POOR, you should tip 15%. If the service is GREAT, you should tip 20%. You can find the tip amount by calculating 15% or 20% of the total bill. (Change percent to decimal, “of” means x)OR you can use mental math tricks!

Use the Hamburger Hut receipt below to calculate how much a 15% tip and a 20% tip would be.

NOTE!!! You are always welcome to leave more than the expected tip. REMEMBER to be kind and generous to those who serve you.

How to estimate a 15% tip:

Step 1: __________

Step 2: __________

Step 3: __________

Step 4: __________

How to estimate a 20% tip:

Two simple ways:

Take

5 to 1 RULE

Round off the total to the nearest dollar.Take 10% of total. Use the 10% shortcut.Take 5% of total. That’s just half of 10%.Add 10% and 5% to make 15%

10% and double it.

For every $5 you spend, leave a $1 tip.

1. A group of friends go to a nice restaurant for dinner. The total bill comes to $64.89.

Calculate a 15% tip.

Calculate a 20% tip.

If the service was poor, what amount would you leave as a tip and why?

If the service was wonderful, what amount would you leave as a tip and why?

2. A couple of friends go out to eat at a restaurant in town. Their bill comes to $49.41. Some of the dishes were tasty, but one was not very warm. The server mixed up someone’s order and you had a tough time getting their attention when you needed a drink refill. Approximately what should the tip be? Explain your thinking.

3. A couple go out to eat at a restaurant, and their total bill comes to $32.64. The food was great, the server was attentive and refilled their drinks without even being asked. Approximately what should the tip be? Explain your thinking.

Percent of Change

A percent of change indicates how much a quantity increases or decreases with respect to the original amount.

The percent of change is the ratio of the amount of increase or decrease to the original amount.

It’s very similar to the proportion . The “part” is the change. The “whole” is the original amount.

The change may be more or less than the original amount.

If the new amount is greater than the original amount, the percent of change is called a _______________________.

If the new amount is less than the original amount, the percent of change is called a __________________________.

For example, let’s say someone originally earned a wage of $25 per hour, then gets a raise and now earns $30 per hour. To find the percent of increase, you first have to find the amount of the change. You don’t actually use the $30 in the proportion itself. You subtract $25 from $30 to get a “change of $5.” Then you set up the proportion:

Then solve. (One in disguise/Cross-products)

The percent of change is 20%. Since the wage increased, we can say the “percent of increase was 20%.”

amount of change percent of change

original amount 100

part %

whole 100

amount of change percent of change

original amount 100 5

25 100

percent of increasepercent of

decrease

1. Find the percent increase from 150 to 189.

2. Find the percent decrease from 512 to 320.

3. The High-Tech Math Store is having a sale on all their calculators. The original cost of a graphing calculator was $120.00. It is on sale for $90.00. What is the percent of discount?

4. The original amount:

The NEW amount:

Find the percent of increase or decrease.

5. Sydney bought a pair of shoes that were on sale. She paid $90 (not including tax). If she had purchased the shoes while they were NOT on sale, she would have paid $110 (not including tax). What was the percent discount she received?

6. THINKER! Last summer John hit 25 home runs. If he increases this number by 20% next year, how many home runs can he expect to hit?

Simple InterestWhen you know the principal amount, the rate and the time, the amount of interest can be calculated by using the formula:

I = PRT I = P x R x T

Principal:

Rate of interest:

Time:

1.Sam puts $700 in a savings account that offers 4% simple interest.

How much interest will he earn after two years? What will his new account balance be?

For example, we have $4500.00 to invest (or to borrow) with a rate of 9.5% for a 6 year period of time.

Interest = 4500 x .095 x 6

nterest

rincipal

ate

ime

Amount of money you start with (in the account or the loan)

Change the % to a decimal so you can multiply

Must be in years (turn portions of years into decimals)

2. Devin puts $15,000 into a savings account that offers 3.5% simple interest. Calculate how much simple interest is earned in 6 months. Then calculate how much simple interest is earned in 10 years.

3. A bank offers a loans for $15,000 at an interest rate of 10 ½ % per year. How much simple interest will the bank receive on this loan over a three year period?

4. Compute the interest paid on an account containing $86.45 for 3 ¼ years if the simple interest rate is 0.2%.

5. Maria takes out a simple interest loan to buy a used car. She borrows $12,000 at 6.5% interest for 6 years. The car cost $12,000. What will be the total cost of the car after 6 years?

Percent Mark-Up

Stores buy items from a wholesaler or distributer at _____________________and increase the price when they sell the items to consumers (customers) at ____________________. The increase in price provides money for the operation of the store and the salaries of people who work in the store. The increase is often a percent of the wholesale price. This percentage is called the markup.

This formula is used with calculations involving markup:

Retail Price = Wholesale Price + Markup Note: the “Markup” is actually the “___% of WP”

REMEMBER: change percents to decimals and “of” means multiply.

For example, a street vendor buys bracelets from a manufacturer for $7 each. The vendor marks up the price by 150%. What is the retail price? (How much does the vender sell the bracelet for?)

RP = WP + MURP = $7 + (150% of $7) $7 + (1.5 x $7) $17.50 The retail price is $17.50.

1. The wholesale price of an item is $4.00 and the markup is 25%. Find the retail price.

3. THINKER! A furniture store marks up the wholesale price of a desk lamp by 80%. The retail price is $45. What is the wholesale price?

2. If an item can be purchased at a wholesale price of $125, and is marked up 50%, what is the retail price?

wholesale pricesretail

prices

What is 60% of 420?

A 2.52B 25.2C 252D 2520

40% of what number is 200?

A 500B 240C 80D 50

Multiple Choice Questions

A teacher buys a school sweatshirt at 35% off the original cost. The original cost of the sweatshirt was $40.00, what is the sale price?

A $5.00B $14.00C $26.00D $35.00

A student sells 194 chocolate bars for a fundraiser. If 75% of the bars have nuts, approximately how many chocolate bars have nuts?

A 150B 175C 225D 275

Multiple Choice Questions

Last year, a student paid $50 for a football season pass. This year, a season pass costs $60. What was the percent of increase in the cost of the season pass?

A 10%B 20%C 83%D 120%

A teenager deposits $600 into his savings account at a simple annual interest rate of 3%. How many years would it take him to earn $90 in simple interest?

A 2 yearsB 5 yearsC 20 yearsD 50 years

Multiple Choice Questions