Video: Pack 4 • Paper 1 • Question 12

Pack 4 • Paper 1 • Question 12

05:00

Video Transcript

There is a sale at the end of the farmers’ market. Farmer A 20 percent off normal price, Farmer B one-quarter of normal price. Farmer A’s two-kilogram box of strawberries costs 10 pounds in the sale. Farmer B’s two-kilogram box of strawberries costs 10 pounds 50 in the sale. Which farmer sold strawberries at a greater price before the sale? You must show all your working.

Let’s begin by calculating the cost of a two-kilogram box of strawberries from each farmer before the sale. Farmer A, there’s a number of ways we can perform this calculation. The first is to decide what percentage of the original, the discounted, rate is. If a product is reduced by 20 percent, that means it’s now worth 80 percent of the original price. This is found by subtracting 20 percent from 100 percent since the original is always worth 100 percent. This means then that 10 pounds is worth 80 percent of the original price.

If we want to work out the original price, we need to calculate what 100 percent is worth. To scale down from 80 percent to 20 percent, we can divide by four. Remember dividing by four is the same as halving and halving again. Half of 10 is five and half of five is 2.5. 10 pounds divided by four is two pounds 50. We know then that 20 percent of the original price is two pounds 50.

We can scale this back up to 100 percent by multiplying by five. And we can use the column method to perform that calculation. Zero multiplied by five is zero. Five multiplied by five is 25. So we put a five in this column and we carry the two. Since only one of the numbers in this problem is a decimal, we can carry the decimal points straight down. Two times five is 10. Then, when we add the two, we get 12. That means that two pounds 50 times five is 12 pounds 50. The original price of farmer A’s two-kilogram box of strawberries is 12 pounds 50.

The alternative method can be a time-saver. We form an equation by considering what sum we would have used to work out a 20 percent discount. We already said a 20 percent reduction is the same as finding 80 percent of the original amount. Remember percent means out of 100. So we can multiply the original amount by eighty one hundredths to find the discounted price.

Let’s simplify this fraction by dividing both the numerator and the denominator by 20. Eighty one hundredths simplifies to four-fifths. We can treat this as an equation, which we can solve by multiplying both sides by five. That gives us the original price multiplied by four is 50 pounds.

Finally, we can divide both sides of this equation by four. We said earlier that to divide by four. We can halve and halve again. Half of 50 pounds is 25 pounds and half of 25 pounds is 12 pounds 50. Once again, we found that farmer’s A two-kilogram box of strawberries cost 12 pounds 50 before the sale.

Now, let’s consider farmer B. Farmer B has reduced the price by one-quarter. That means that the new price must be worth three-quarters of the original price since one minus one-quarter is three-quarters. If we knew the original price, we’d multiply then by three-quarters to give us the new price. Forming an equation with this information gives us the original multiplied by three-quarters is equal to 10 pounds 50.

We can solve this equation by multiplying both sides by four. To multiply by four, we can double a number and then double it again. 10 pounds 50 multiplied by two is 21 pounds and 21 pounds multiplied by two is 42 pounds.

Finally, let’s divide both sides of this equation by three. We can use the bus stop method to help us. Four divided by three is one remainder one and 12 divided by three is four. 42 divided by three is 14. This means that farmer B’s two-kilogram box of strawberries costs 14 pounds before the sale.

Since farmer B sold strawberries for 14 pounds before the sale, whereas farmer A sold them for 12 pounds 50, farmer B sold strawberries at a greater price before the sale.

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