APPLICATION OF PERCENT
1. COMMISSION
- When you work for a salary, you receive the same amount of money each week or month. When you
work for a commission, you are paid a percentage of what you sell.
Commission = Commission rate × Total Sales
C=r×T
- As with most formulas involving percent, we need to be sure to convert the percent to either a fraction
or decimal, before plugging in for r.
Example:
1. Joshua’s sales commission rate is 6%. What is the commission from the sale of $65,750 worth of new
car sales?
Solution:
Commission = Commission rate × Sales
C = 6% × 65,750
C = 0.06 × 65,750
C = 3,945.00
So the commission is $3,945.00.
2. Marsha gets paid 12% of all makeup she sells. She made a total of $216 this week from commission.
What was the total sales of makeup for the week?
Solution:
C=rT
216 = 0.12(T)
100(216) = 100(0.12T)
21600 = 12T
T = 21600/12
T = $1800
So Marsha sold $1800 worth of makeup this week for a commission of $216.
PROBLEM SOLVING
1. Tina sells software and is paid a 20% commission on all she sells. If she sold a total of $8000 worth of
software in one month, how much commission did she make from the sale?
2. Maria sells hair products at the mall and is paid a commission on what she sells. If she sold a total of
$860 in hair products and was paid a commission of $154.80, what is her commission rate? Write your
answer as a percent.
3. Jim sells homes and earns a 4% commission on all he sells. If he made a commission of $19,000 on one
home he sold, what was the total price of the house?
4. Rachel sells cars and is paid a commission on what she sells. If she sold a total of $66,400 worth in cars
and was paid a commission of $4,648, what is her commission rate? Write your answer as a percent.
5. Jim sells paintings and earns a 6.5% commission on all he sells. If he made a commission of $279.50 on
one painting he sold, what was the total price of the painting?
2. DISCOUNT
- The amount being deducted from the original price and is usually expressed as rate or percent.
Original Price (OP) – this is the marked price or list price
Discount (D) – the amount being deducted from the original price
Selling Price (SP) – the resulting amount after the discount had been deducted from the original price
Discount = Selling Price – Original Price
D = SP – OP
Discount
𝐑𝐚𝐭𝐞 𝐨𝐟 𝐃𝐢𝐬𝐜𝐨𝐮𝐧𝐭 = × 100%
Original Price
Example:
A bag is being sold at Php 390.00. If its original price is Php 600.00, find the rate of discount.
Solution:
Solve for the discount in order to get the rate of discount.
𝐷 = 𝐷𝐷 − 𝐷𝐷
𝐷 = 600 − 390
𝐷 = 210
Therefore, discount is P210.
Substitute the values to the formula for rate of discount.
210
Rate of Discount = × 100%
600
Rate of Discount = 35%
The rate of discount is 35%.
PROBLEM SOLVING
1. After a 15% discount, how much should a shirt originally sold at P440 cost?
2. A car has a regular price of $18000 and is on sale for $14,400. What was the discount rate? Write your
answer as a percent.
3. During the midnight sale in Gaisano Capital, the pair of Jag pants with an original price of P1,200 is now
being sold at 35% discount. For how much is the pants sold?
4. A bicycle that regularly sells for $350 is on sale for 25% off. What will the sales price be?
5. If Oscar bought some patio furniture that regularly sells for $275 on sale for $192.50, what was the
discount rate? Write your answer as a percent.
6. Tyrone bought a shed to put in his backyard. If the shed was on sale for 20% off and the sale price was
$360, what was the regular price of the shed before the sale?
7. Tara bought a necklace that regularly sells for $450 on sale for $315, what was the discount rate? Write
your answer as a percent.
8. Rick bought a book on sale for 40% off and the sales price was $30. What was the regular price of the
shed before the sale?
3. SALES TAX, PROFIT AND MARK-UP
- Sales tax is an additional amount of money charged on certain goods and services.
- Profit is the positive gain remaining for a business after all costs and expenses have been deducted
from total sales. Profit is also referred to as net profit, net earnings or net income.
- When profits are based on cost, profit is commonly referred to as mark-up over selling price, and the
percent profit on cost is called percent mark-up.
Sales Tax = Sales tax rate (as a decimal) × Purchase price
Total price = Purchase price + Sales tax
Example:
1. How much sales tax is charged on an item that costs $250 if the sales tax rate is 6%? What is the total
price of the item?
Solution:
We will multiply the sales tax rate as a decimal and the purchase price in order to calculate the
amount of sales tax.
Sales tax = .06 ∗ $250 = $15.00 or $15
Thus, the amount of sales tax is $15.
To compute the total price of the item, we will add the purchase price and the amount of sales
tax together.
Total price = $250 + $15 = $265
Thus, the total price of the item is $265.
2. The sales tax is $140 on the purchase of a new dining room set which cost $1,750. What is the sales tax
rate?
Solution:
140
Sales tax rate = 1750 × 100
Sales tax rate = 8%
Thus, the sales tax rate is 8%.
PROBLEM SOLVING
1. Tim bought a washing machine for a total of $651 with tax included. What was the price of the washing
machine before tax if Tim lives in an area with an 8.5% sales tax rate?
2. Julie wants to buy an iPhone that costs $120 before tax. If Julie lives in an area with a 9.25% sales tax,
what will be the total price of the iPhone with tax included?
3. Lianna bought a turtleneck sweater for $19.71 with tax included. If the price of the sweater before tax
was $18, what is the sales tax rate in Lianna’s area? Write your answer as a percent.
4. Wade works for a store that sells computers and computer parts and has a 20% markup policy. If they
bought a computer from the manufacturer for $790, how much will they sell it for after the markup?
5. Patricia works for a clothing store. If the store buys its sweatshirts from the manufacturer for $19 and
then sells them for $28.50, what is the stores markup rate? How much is the store’s profit from selling
sweatshirts?
3. INTEREST
- Interest is the amount paid for the use of money.
- Principal is the money that is borrowed.
- Interest rate is the percentage charged on the basis of one year's use of the money.
- Time is the number of days or months or years for which the money is being borrowed and interest is
calculated.
Simple Interest = Principle × Rate × Time
I=P×r ×t
Example:
Thomas earned $65.25 simple interest for one year on an investment of $900. What annual rate of
interest was paid?
Solution:
simple interest = $65.25
time = 1 year
principal investment = $900
𝐼
r=
𝑃𝑡
65.25
r=
900(1)
r = 7.25%
The annual rate of interest is 7.25%
PROBLEM SOLVING
1. Kai invested $3000 into some stocks that yielded a 6.8% interest rate. How much simple interest did
she make after 2 years?
2. Simon invested $2600 into a simple interest account for 2 years. If the account yielded $234 at the end
of two years, what was the interest rate? Write your answer as a percent.
3. Elena invested some money into a bond account that yielded $375 in interest at the end of 1 year. If the
interest rate was 3%, how much did she originally invest?
4. Jessica invested $5000 into a simple interest savings account that yields 6.5% simple interest. How
many years will it take for her to make $1300 in simple interest?
5. Simon invested $3500 into a simple interest account for 2 years. If the account yielded $385 at the end
of two years, what was the interest rate? Write your answer as a percent.
6. Rick invested $4,000 into a bank account that earns 6% simple interest. How long will it take Rick to
make $720 in simple interest?
7. Jerry deposited $3500 into a simple interest account. He was able to earn $122.50 in interest after 6
months (1/2 year). What was the interest rate the bank used? Write your answer as a percent.
8. What is the simple interest on a principal of $6,500 invested at an interest rate of 9% for six months?
9. Leila had a savings deposit of P150,000 in PHCCI 10 years ago. The teller told her that her money grew
by 8.5% as of today. How much does she have in her savings account now?
