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
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
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