Video: FP1P3-Q03

FP1P3-Q03

05:01

Video Transcript

Two stores both have offers on bouquets of flowers. Store 𝐴: Buy four and get one additional bouquet free. Store 𝐵: All bouquets are 15 percent off. Usually, a bouquet in either store costs 15 pounds. Billy wants to buy 10 bouquets. Which store offers a better offer on buying bouquets? Show all your working.

To answer this question, we need to work out the cost of buying 10 bouquets from each store. We’ll start with store 𝐴. Store 𝐴’s offer is that if you buy four bouquets, you actually get five, because you get one additional bouquet free. This means that if Billy buys eight bouquets, she’ll actually get 10, as she’ll get two free, one for each lot of four that she’s bought. So this means that we need to find the cost of buying eight bouquets from store 𝐴 as we’ll actually get 10.

As each bouquet in store 𝐴 costs 15 pounds, the total cost is found by multiplying 15 by eight, which gives 120. So the total cost of buying 10 bouquets from store 𝐴 is 120 pounds.

Now let’s consider the cost for store 𝐵. Store 𝐵 doesn’t offer any free bouquets, so Billy will have to pay for 10. But she gets 15 percent off the cost of each bouquet. We need to find the reduced cost of each bouquet from store 𝐵. And we could do this in a number of different ways.

The first way is we could find 15 percent of the cost of each bouquet and then subtract it from the price of 15 pounds. There are also lots of different ways that we could find 15 percent of a number. The first is we could find one percent by first dividing it by 100. 15 divided by 100 is 0.15. To scale up from one percent to 15 percent, we’d then need to multiply by 15. We have 0.15 multiplied by 15, which, using a calculator, is equal to 2.25.

Another way to find 15 percent of a number is to use a decimal multiplier. We can first write 15 percent as a fraction. It’s equal to 15 over 100. We then convert this to a decimal. To divide 15 by 100, we can keep the decimal point fixed and move the digits two places to the right, giving 0.15. To find 15 percent of 15, we can then multiply 15 by this decimal multiplier. 0.15 multiplied by 15 gives 2.25, as before. Whichever method we used for finding 15 percent, we don’t have to subtract this from 15 pounds, as remember it’s 15 percent off the original price. 15 pounds minus two pound 25 gives 12 pounds 75. So this is the sale price of each bouquet in store 𝐵.

There is actually a third way that we could have calculated this sale price. 100 percent minus 15 percent is 85 percent. So this means that the sale price of each bouquet is 85 percent of the original price. We could then convert this to a decimal multiplier. 85 percent as a fraction is 85 over 100. And as a decimal, this is equivalent to 0.85.

Remember, we keep the decimal point fixed and move the digits two places to the right. We could then work out the sale price of each bouquet in store 𝐵 by multiplying the original price of 15 pounds by this decimal multiplier of 0.85. And it gives the same price of 12 pounds 75 as we’ve just calculated. Any of these methods will be absolutely fine. It just depends which one makes the most sense to you.

Now that we found the cost of each bouquet, we need to find the total cost. Remember, there are no free bouquets in store 𝐵, so we need to pay for all 10. We therefore multiply the cost of 12 pounds 75 by 10, and it gives 127 pounds and 50 pence.

Another way of working out the total cost for store 𝐵 would’ve been to find the cost of 10 bouquets first and then apply the 15 percent discount at the end. And it would also have given us the same result.

Now that we’ve worked out the cost for each store, we can compare them to see which offer is the better offer. The total cost for store 𝐴 is 120 pounds, and the total cost for store 𝐵 is 127 pounds 50. As 120 pounds is less than 127 pounds 50, which remember is what is meant by this inequality symbol that I’ve put between the two amounts, this means that store 𝐴 has the better offer for buying 10 bouquets.

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