Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 3

GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 3

04:03

Video Transcript

Lara buys the following items for a picnic: three sandwiches costing 1.40 each; six apples costing 60 pence each; and two bottles of the same soft drink. She pays with a 20-pound note and receives nine pound change. She works out that a bottle of soft drink costs 1.50. Is she correct? You must show all of your working out.

Okay. So in this question, we’ve been told the cost of each sandwich and the cost of each apple, but not the cost of each bottle of soft drink. And we are asked to work out whether what Lara says is correct. We’re told that Lara pays with a 20-pound note and receives nine pounds change. Which means that the total cost of the item she bought can be found by subtracting nine pounds from 20 pounds, which gives 11 pounds.

Now, this total cost will be made up of the cost of the sandwiches plus the cost of the apples plus the cost of the drinks. And so, we need to work out first the total cost of the sandwiches and the total cost of the apples, so we can see how much is left over for the drinks.

To find the cost of the sandwiches, we need to multiply three by 1.40. We could do this using a column multiplication method. And as only one of the numbers that we’re multiplying is a decimal, the decimal point in our answer will go directly below the decimal point in 1.40.

First, we multiply zero by three which gives zero. Then, we multiply four by three which is 12. So we put a two and carry a one into the next column. Finally, we multiply one by three which is three. And adding the one that we’ve carried gives four. So the total cost of the sandwiches that Lara bought is 4.20.

Another way to do this calculation would be to split 1.40 up into one pound and 40 pence. Three multiplied by one pound is three pounds. And three multiplied by 40 pence is 120 pence or 1.20. We could then add these values together to give the same answer of 4.20.

Next, we need to work out the cost of the apples. And there are six of them, each costing 60 pence. So we need to multiply six by 60 pence. The easiest way to do this without a calculator is to think of 60 as six multiplied by 10. So our calculation becomes six multiplied by six multiplied by 10 pence. We can multiply numbers in any order. So if you multiply six by six, first of all, this gives us 36. And then, multiplying by the 10 gives 360. So the total cost of the apples is 360 pence. As there are 100 pence in a pound, this cost in pounds is 3.60.

Next, we can add together the cost of the sandwiches and the apples using a column addition method. And it gives 7.80 or 7.80. Now, Lara thinks that each bottle of soft drink costs 1.50. But remember, she bought two of them. So two bottles would cost three pounds. We can either work this out using a column multiplication method. Or, we could just double 1.50 mentally. And we would see that it equals three pounds.

If Lara is correct, then when we add this cost of three pounds on to the cost we’ve already found for the sandwiches and apples, we should get the total cost of all of the items, which was 11 pounds. However, if we use a column addition method to add 7.80 to three pounds, it gives 10 pounds 80, not 11.

So we can conclude then that Lara is not correct because the cost of 1.50 per bottle of soft drink would give the wrong total when we add it to the cost of three sandwiches and six apples.

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