Introduction
When dealing with money, it is important to keep track of how much you have, earn or spend. In addition to this, things like discounts and determining best buys can be calculated so that you always know exactly what the numbers are when buying or selling.
Profit and loss
When dealing with financial situations, there are a few terms that are often used.
The cost price of an item is how much money you need to spend to get it. Multiple cost prices can be referred to collectively as expenses.
The sale price of an item is how much money you earn by, well, selling it. Money earned can be more generally referred to as money received or revenue.
The profit made on an item is the difference between the sale price and the cost price. A profit is only made if the sale price is greater than the cost price.
The loss incurred from an item is the difference between the cost price and the sale price. A loss is only made if the cost price is greater than the sale price.
Profit and loss can be calculated using the formulas: \begin{aligned} \text{Profit}&= \text{Sale price}-\text{Cost price} \\ \text{Loss}&=\text{Cost price}-\text{Sale price} \end{aligned}
Examples
Example 1
Calculate the profit (or loss) when:
The selling price is \$303 and the cost price is \$276.
The money received is \$4786.71 and expenses are \$5653.17.
Profit and loss can be calculated using the formulas: \begin{aligned} \text{Profit}&= \text{Sale price}-\text{Cost price} \\ \text{Loss}&=\text{Cost price}-\text{Sale price} \end{aligned}
Discounts and mark ups
Discounts and mark ups are percentage decreases and increases of item prices respectively. When an item has its price discounted, the cost price of that item is decreased by some percentage. When an item has its price marked up, the cost price of that item is increased by some percentage. We can calculate the effect of discounts and mark ups in the same way that we would calculate  percentage changes to a value.
Since discounts and mark ups are multiplicative changes to the cost price, multiple discounts and/or mark ups can be applied to a cost price in any order without changing the final result.
Examples
Example 2
A TV player normally sells for \$1498.44, but is currently on sale. In each of the following scenarios, calculate the percentage discount correct to two decimal places.
The TV player is discounted by \$144.90.
The TV player is on sale for \$1148.84.
Example 3
A set of professional knives for chefs originally cost \$1600 and is on sale at 20\% off. A chef receives a further 9\% trade discount after the sale discount is applied.
What is the final cost of the set to a chef?
How much overall would be saved in comparison to the original price?
What overall percentage discount is this equivalent to?
To find a percentage discount, we can use the formula: \text{Percentage discount}=\dfrac{\text{discount }}{\text{original price}}\times 100\%
Best buys
When presented with two different prices for the same product, it is helpful to know which is greater and which is smaller. However, comparing the price of a 300 mL can of drink to a 2 L bottle of the same drink is not very useful since their costs are relative to their different quantities. In order to properly determine which is the best buy, we want to calculate their prices with respect to some common amount.
Suppose that the 300 mL can costs \$0.45 and the 2 L bottle costs \$2.90.
To properly compare these prices, we can find the costs of the can and bottle as rates of dollars per litre.
The can costs \$0.45 per 0.3 L, which can be expressed as \dfrac{0.45}{0.3} dollars per litre, which we can simplify to be \$1.50 per litre.
The bottle costs \$2.90 per 2 L, which can be expressed as \dfrac{2.90}{2} dollars per litre, which we can simplify to be \$1.45 per litre.
From our calculations, we can see that the bottle is the better buy, since it has a lower cost price per litre.
We can perform similar calculations for any situation where the same product is being sold in different quantities for different prices.
Examples
Example 4
A supermarket sells two different brands of eggs, Sunny Side Up and Classy Chooks:
Sunny Side Up eggs cost \$7.70 for 11 eggs.
Classy Chooks eggs cost \$2.10 for 7 eggs.
Find the cost in cents per egg from Sunny Side Up.
Find the cost in cents per egg from Classy Chooks.
Which brand sells its eggs at a cheaper price?
In order to properly determine which is the best buy, we want to calculate their prices with respect to some common amount.