# CSEC Mathematics: Consumer Arithmetic- Discounts

Consumer arithmetic is all about basic calculations made in day to day business transactions and budgeting. In this section, we will discuss discounts.

Throughout this lesson, you will hear a few terms that you may be unfamiliar with:

**Marked Price (MP)- **The price of an item written on the price tag.

**Selling Price (SP)- **This is the price for which the item will be sold to the consumer, inclusive of markups or discounts. It can require several different calculations to find the selling price based on what the question is asking.

**Discount**

Stores and businesses will often advertise discounts as promotion for their business and encouragement for customers to buy more, for example, 15% off everything or 20% off all premium plans. A **discount **is a reduction from the marked price.

To find the discount, you simply subtract the selling price from the marked price.

**Discount= MP-SP**

Transposing this also gives us other important relationships:

**MP= Discount + SP**

**SP= MP- Discount**

__Example 1:__ In the supermarket one day, you pick up a box of pop tarts with a marked price of $560.00. However, upon going to pay for it, you realize that there is a store-wide discount and only pay $448.00. What is the discount?

**Discount= MP-SP**

** = $560.00-$448.00**

** = $112.00**

**The discount is $112.00.**

It is also necessary for you to know how to express the discount as a percentage:

**% Discount= (MP-SP/MP) x 100**

** = (Discount/MP) x 100**

__Example 2:__ Jim goes to his local pet store to purchase a can of fish food. The marked price of the fish food is $300.00, but he only pays $255.00 due to a store loyalty discount he receives. What is the percentage discount?

**% Discount= (MP-SP/MP) x 100**

** = ($300.00-$255.00/$300.00) x 100**

** = ($45.00/$300.00) x 100**

** = 15%**

**Therefore, Jim receives a discount of 15%.**

Given the percentage discount and the marked price, you should also be able to calculate the selling price.

**SP= MP-(%Discount/100 x MP)**

__Example 3:__ Your mother goes shopping online for back to school supplies for you on Amazon. They are having a sale of 25% off on all school shoes, so your mother buys you a pair of black school shoes with a marked price of $9800.00. What is the price she pays with the discount applied?

**SP= MP-(%Discount x MP/100)**

** = $9800.00-(25/100 x $9800.00)**

** = ****$9800.00-$2450.00 **(here, you are subtracting the discount from the marked price)

**= $7350.00**

Your mother pays $7350.00 for your school shoes.

CSEC also requires that you are able to find a value based on the other values you have been given.

__Example 4:__ You purchase a pack of cards for $400.00. This price is inclusive of a discount of 15%. What was the marked price?

Sometimes, the easiest way to work out these types of questions is through proportions:

**(100-15/100) = (400/MP) **Here, we equate the percentage of the marked price that is
the selling price to the selling price of the marked price.

**(85/100) = (400/MP) **Cross multiplying, we get:

**85 x MP = 100 x 400**

**85 x MP = 40000**

**MP= 40000/85**

**MP= $470.59**

Here is a useful __website to learn a bit more about discounts__.