Sometimes businesses want to attract customers by lowering the price and giving a discount, which is usually expressed in percentages. We've just seen in this chapter how to calculate percentage increases and decreases, usually the hardest part is interpreting the word problems and what they mean mathematically.
Worked example
Example 1
Lisa wants to buy a new phone for $\$360$$360, and was delighted to find out that she gets a $20%$20% discount. Calculate the value of the discount and hence the price Lisa pays for the phone.
Think about which numbers are the ones you need, and the meaning of 'value'. Value means how much the discount actually is in terms of money.
Do: That means we need to calculate $20%$20% of $\$360$$360.
| $360\times20%$360×20% | $=$= | $72$72 |
Therefore the discount is $\$72$$72.
This would mean the final price Lisa pays would be $\$360-\$72=\$288$$360−$72=$288
Remember to always attach the correct unit to your final answer, whether they're dollars, pounds or in other questions maybe even kilograms or metres.
Practice questions
Question 1
Steph is going to buy a hat that is marked as $25%$25% off. The original price was $\$36$$36.
What is the value of the discount in dollars?
What is the price that Steph will pay for the hat?
Question 2
The full price is $\$300$$300. Yvonne receives a discount of $55%$55%.
How much would a $10%$10% discount be?
How much would a $5%$5% discount be?
Hence find the discount that Yvonne receives.
Terminology in percentage questions
1. Discount: how much the cost of something is reduced by. Eg. a $10%$10% discount on $\$200$$200 means taking $10%\times\$200=\$20$10%×$200=$20 off the full price of $\$200$$200
2. Commission: how much money a salesperson earns. It is usually a percentage of how much they manage to sell. Eg. $50%$50% commission on $\$10$$10 worth of sales is $50%\times\$10=\$5$50%×$10=$5, which is how much the salesperson gets to keep.
3. Profit: if an item is sold for more than what it cost to make or obtain, you make a profit. So it is the difference between the selling price and the cost price. Eg. If I bought a bike for $\$10$$10 and sold it for $\$15$$15, my profit is $\$5$$5
4. Loss: if an item is sold for less than what it cost to make or obtain, you make a loss. So it is the difference between a product's sale price and buy price when the sale price is lower. Eg. If I bought a bike for $\$20$$20 and sold it for $\$18$$18, my loss is $\$2$$2
5. Stocks: a type of 'virtual' product which represents ownership of part of a company
6. Percentage profit/loss: the profit/loss as a percentage of the buying price. Eg. I bought a bike for $\$20$$20 and sold it for $\$22$$22, so my percentage profit is $\frac{22-20}{20}\times100%=\frac{2}{20}\times100%$22−2020×100%=220×100% = $10%$10%. A profit of $\$100$$100 sounds good, but is it really that great if the buying price was $\$100000$$100000?
7. Interest: if you have savings in a bank account, or owe money in the form of loans, interest is the amount by which the savings or loans grow. Eg. If I have $\$500$$500 in the bank and the interest rate offered is $10%$10%, I will earn an extra $10%\times\$500=\$50$10%×$500=$50 worth of interest.
Practice questions
Question 3
A sales assistant is paid a commission of $15%$15% on her weekly sales. Find her commission for a week in which she sells products to the value of $\$2000$$2000.
Question 4
Luke deposits $\$8635$$8635 in a bank for one year. If the interest rate is $7%$7% p.a:
How much interest, in dollars, did Luke earn for the year? Write your answer to the nearest cent.
Find the total amount (to the nearest cent) in his bank account at the end of the year.