Every business is trying to sell something, and the way they display their prices can be confusing. Sometimes they can be deliberately confusing. By using some mathematical strategies we can compare two or more different offers and determine the best buy.
If the two options we are choosing between involve different quantities, we can use what we know about rates to find out how much a single unit costs.
Isabelle is buying juice for her nephew's birthday party. A 3.2 \text{ L} bottle of apple juice costs \$13.76. A 2.1 \text{ L} bottle of orange juice costs \$6.30.
How much does apple juice cost per litre?
How much does orange juice cost per litre?
Which juice is the best buy?
In choosing between two options, we can find the cost per unit to determine which is the better buy.
We can also compare prices by determining how much a single dollar buys. The idea is very similar to the previous one.
A 1.35 \text{ kg} packet of mince costs \$15. How many grams of mince does each dollar buy?
We can also compare prices by determining how much a single dollar buys.
Notice that when using this method, the rate with the larger unit value represents the better value, as we get more for the same price.
Stores frequently offer a percentage discount on items which converts the original price into a sale price. This discount is often presented as "30\% off" or "reduced by 25\%", and it is important to know how to calculate the new price.
When a sale price has a percentage discount applied, we find that percentage of the original price and subtract it to find the sale price: \text{Sale price}=\text{Original price}-(\text{Original price}\times\text{Discount percent})
We can take a shortcut by thinking about what happens after the discount is applied. If an item is reduced by 30\%, then the sale price is 70\% of the original price. Similarly, a 25\% discount means the sale price is 75\% of the original price. The remaining percent is 100 minus the discount.
A pair of Bevi jeans normally costs \$120, and the store is offering a 20\% discount. A similar pair of Genie jeans normally costs \$150, and the store is offering a 30\% discount. Which pair of jeans is the best buy?
When a sale price has a percentage discount applied, we find that percentage of the original price and subtract it to find the sale price: \text{Sale price}=\text{Original price}-(\text{Original price}\times\text{Discount percent})
We can also use a shortcut by multiplying the original price by the remaining percent which is 100\% minus the discount percentage.