Reverse Percentages: Calculate Original Amounts Easily
Master the art of reverse percentages by learning how to calculate the original amount when a percentage of a quantity is known. Explore examples and handy techniques to work through such problems efficiently. From determining the value of items sold to finding the original price of discounted items, these illustrative examples will strengthen your understanding and problem-solving skills in reverse percentages.
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01 March 2025 Reverse percentages LO: To calculate the original amount if we know a percentage of a quantity. www.mathssupport.org
Reverse percentages In many situations we are given the final amount after a percentage has been added or subtracted and we have to find the original amount. If we know a percentage of a quantity, we can calculate the original amount. To solve this type of problems we need to work in reverse. We let a variable represent the original amount, then construct an equation which relates it to the final amount. www.mathssupport.org
Reverse percentages Example 1 Randy receives 5% commission on the items she sells. In one week she earns 140 commission. Find the value of the items she sold. To solve this type of problems we need to work in reverse. We let a variable represent the value of the items, construct an equation which relates it to the final amount. then Let v be the value of the items she sold. 140 is the 5% commission, in other words it is 5% of the total value (v). 0.05 v = 140 140 0.05 2800 v = p = www.mathssupport.org
Reverse percentages Example 2 I bought a jacket in a sale. It has 15% off and I only paid 25.50 for it. What is the original price of the jacket? To solve this type of problems we need to work in reverse. We let a variable represent the original amount, construct an equation which relates it to the final amount. then Let p be the original price of the jacket. 25.50 is the price after 15% reduction, in other words 85% the original price (p). 0.85 p 25.50 = 0.85 p p = 25.50 0.85 30 p = www.mathssupport.org
Reverse percentages Example 3 An mp3 player is increased in price by 35%. The selling price is 240.30. What was the original price of the mp3 player? To solve this type of problems we need to work in reverse. We let a variable represent the original amount, then construct an equation which relates it to the final amount. Let p be the original price of the mp3 player. 240.30 is the price after 35% increase, in other words 135% the original price (p). 1.35 p 240.30 = 1.35 p 240.30 1.35 178 p = p = www.mathssupport.org
Reverse percentages Example 4 We can also use a unitary method to solve these type of percentage problems. For example, We can also use a unitary method to solve these type of percentage problems. For example, Christopher s monthly salary after a 5% pay rise is 1312.50. What was his original salary? The new salary represents 105% of the original salary. 105% of the original salary = 1312.50 1312.50 105 1312.50 105 1% of the original salary = 100 100% of the original salary = Original salary = 1250 www.mathssupport.org
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