☰ Year plan · Mathematics

Applications of ratio and proportion

Week 2 · Applications of ratio and proportion: scale drawings, sharing in a ratio, discounts and tax · 3 lessons
3

Percentage applications: discount, tax and finding the original price

Mathematics Prep 1 Term 1, Unit 1, Lesson 2
GoalFind a discount, a price after tax or profit, and an original price from the sale price.
New words
discount · the amount taken off the pricesale price · the price after the discountsales tax · extra money added to a price, by a rate such as 14%original price · the price before a discount
Explanation

Discount = price × rate. A 25% discount on 400 LE is 400 × 25/100 = 100 LE, and you pay 400 − 100 = 300 LE. After a d% discount you pay (100 − d)% of the original price, so a 20% discount means you pay 80%. To find the original price from the sale price, divide by (100 − d)% and multiply by 100. Sales tax of 14% is added to the price before tax: tax = price × 14/100, total = price + tax, or price × 114/100. Note that 14% is the rate and the tax itself is a number of LE.

ƒFormula
sale price = original × (100 − d)%
Tax: total = price × (100 + 14)%.
Worked examples
A jacket costs 400 LE and has a 25% discount. Discount = 400 × 25/100 = 100 LE. Price to pay = 400 − 100 = 300 LE. Check: 75% of 400 = 300.
Original20%80% = 240 LE100%
A shirt costs 240 LE after a 20% discount. It is 80% of the original price. 240 ÷ 80 = 3 LE for 1%, so the original price is 3 × 100 = 300 LE. Check: 20% of 300 = 60 and 300 − 60 = 240.
Price before taxRateTaxTotal
2,500 LE14%350 LE2,850 LE
A tablet costs 2,500 LE before tax and the sales tax is 14%. Tax = 2,500 × 14/100 = 350 LE. Total = 2,500 + 350 = 2,850 LE. The same total comes from 2,500 × 114/100.
Class activity

Sale shopping. With a grown-up, choose three things at home with a price (or make up prices). Imagine a 10% sale, a 20% sale and a 50% sale. Write the price you would pay each time. Which sale saves the most on the dearest thing?

Practice
1
Shoes cost 600 LE and have a 15% discount. How much do you pay?
2
A bag costs 351 LE after a 10% discount. What was the original price?
3
A fridge costs 800 LE before tax. Find the 14% sales tax and the total.
4
A shopkeeper buys a chair for 200 LE and sells it with a 30% profit. What is the selling price?
5
Salma says a 20% discount on 150 LE gives the price 150 − 20 = 130 LE. What is wrong?