Solving Percent Problems

Solving Percent Problems

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​by: Mrs. Grace I. Dorado

​ In this lesson, you will apply what you have learned in finding the Percentage, Rate, and Base.

​ At the end of this lesson, you will understand how to solve problems involving percent problems like problems involving discounts, original price, rate of discount, sale price, mark- up price, commission, sales tax, and simple interest.

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The following terms are used in dealing discount problems:

-Discount (D) is decrease in the price of an item. It refers to the amount to be deducted from the original price.

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-Original Price (OP) is the regular price charged of the item.

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​-Discount Rate (DR) is the percent taken off from the original price.

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​-Sale Price (SP) is the net price or discounted price. It is the price of the item the discount has been deducted.

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​Discount and Sale Price both represent percentage, original price represents the base and discount rate represents the rate.

Example 1: Solving for Discount and Sale Price

​ A dress was sold for Php 500.00 at a 16% discount. How much is the discount or how much can be save? How much is the selling price?

​Formula in finding the discount:

Discount (D)= Discount Rate (DR) x Original Price (OP)

D= DR x OP

Using the Sale Price formula, you have:

Sale Price (SP)= Original Price (OP) - Discount (D)

SP= OP - D

Example 2: Solving for Original Price

A wristwatch was sold for Php 2500.00 with a 20% discount. What was the original price of the wristwatch?

Solution: DR=20% SP=2500 OP=?

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Using the formula for sale price, we have:

Sale Price (SP)= Original Price (OP) x (100%- DR)

SP= OP x (100- DR)

In some instances, the seller add a particular amount on the items or goods to be sell for the profit. From the original price, the mount added is the markup price and the new amount is called the selling price.

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Markup and selling price represent both the percentage, cost represent the base, and the markup rate represent the rate.

​Markup (M) is the increase in the price of an item.

Markup Rate (MR) is the percent to be added to the cost of item.

Cost (C) is the original amount of the item.

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Example 3: Solving for Markup Price

To have the profit, the business woman adds a markup price of Php 4.00 on all the plastic products that bought in divisoria. What is the markup rate of the plastic bottle if the cost is Php 50.00? What will be the markup or selling price?

Using the formula for Markup price, we have:

MR=(M+C)x 100%

Using the formula for Selling Price:

SP= C + M

When someone sell your product, you need to give him some amount of money for his effort or certain percentage for the sales. The percent or amount that he/she will receive is called commission.

The commission and sale proceeds both represent percentage, total sales represents the base and the commission rate represents the rate.

Commission (C) is an amount of money a person receives for selling something.

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Total Sales (TS) is the total amount of sales made by the salesperson.

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Commission Rate (CR) is the percent taken off from the selling price.

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Sale Proceeds (SP) is the amount that remains after the deduction of the commission.

Example 4: Solving for Commission

Mr. Lazo, a car agent receives an 8% commission on the car he sells. What is his commission if he sold a car at Php 1, 550,000.00?

How much will be the sale proceeds?

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Using the commission formula, we have:

C=TS x CR

Using the sale proceeds formula, we have:

SP=TS- C

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Example 5:

Mr. Lazo was given a commission of

Php 120,000.00 of 6% commission rate for selling a house and lot. How much is the total sales of the house and lot that he sold?

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Using the total sales formula, we have:

TS= C + CR

Sales Tax

When you buy some products in the fast food, supermarkets, and other store, you will noticed on your receipt that there is Value Added Tax or (VAT) or sales tax.

In the restaurant, the family ordered foods that has a total amount of

Php 856.00 plus 12% sales tax. How much is the sales tax? How much is the total amount paid to the cashier?

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Using the Sales Tax formula, we have:

Sales Tax= Total Price x Rate of Sales Tax

ST= TP x RST

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Computing the total amount to be paid:

Total Amount= Total Price + Sales Tax or TA= TP + ST

Simple Interest

When your mother or father deposit their money in a savings bank, the bank will pay them a small amount for using their money. This amount is called interest.

Interest (I) is an amount of money earned for using another's money over a

period of time.

​Principal (P) is the amount of money deposited, invested or borrowed.

​Rate of Interest (R) is the percent added to the principal, amount borrowed or invested.

Time (T) is the length of time which money has been deposited or borrowed. It always computed in terms of year.

Amount Due (AD) is the total amount to be paid or received after a certain period of time that the principal has been borrowed or deposited.

Example 6: Solving for Simple Interest

Mr. Lazo opens a savings account in Commercial Bank where the money earns 1.8 interest per year. If he has Php 9,500.00 in his savings account, how much interest will his money earn in 1 year?

Using the interest formula, we have:

I=P x R x T

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Example 7: Solving for Principal

Deo Lagario borrowed money from the lending company of 6% interest. If he paid an interest of Php 450.00 after 19 months, how much money did he borrow?

Using the principal formula, we have

P= I/ RxT