Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 1 • Question 8

At a fairground, Simon has won five tokens. Each token represents 100 credits. He decides to exchange his credits for two different types of sweets: cola bottles and gobstoppers. The table shows the number of credits required for a cola bottle and a gobstopper. He buys 20 cola bottles, as many gobstoppers as possible, and with any change buys extra cola bottles. How many cola bottles and gobstoppers does Simon buy?

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Video Transcript

At a fairground, Simon has won five tokens. Each token represents 100 credits. He decides to exchange his credits for two different types of sweets: cola bottles and gobstoppers. The table shows the number of credits required for a cola bottle and a gobstopper. He buys 20 cola bottles, as many gobstoppers as possible, and with any change buys extra cola bottles. How many cola bottles and gobstoppers does Simon buy?

There is a lot of information in this question. So it is important to write our answer clearly and in a logical order. The first two lines tell us that Simon won five tokens and that each token represented 100 credits. Multiplying five by 100 gives us 500. This means that Simon has 500 credits altogether.

He is exchanging these credits for two sweets: cola bottles and gobstoppers. Firstly, we’re told that he buys 20 cola bottles. As each cola bottle is worth five credits, we need to multiply 20 by five. 20 multiplied by five is equal to 100. Therefore, Simon uses 100 credits to buy these 20 cola bottles. As he initially had 500 credits and he has now used 100, he has 400 credits left. 500 minus 100 is equal to 400.

Next, we were told that Simon bought as many gobstoppers as possible. Each gobstopper was worth 23 credits. We need to work out how many 23s there are in 400. This is the same as saying 400 divided by 23. You could do this using long division. However, we will use the chunking method as it will be easier when dividing by 23.

23 multiplied by 10 is equal to 230. Therefore, Simon can get 10 gobstoppers for 230 credits. To calculate 23 multiplied by five, we could halve this answer of 230, as five is half of 10. One-half of 200 is 100, and one-half of 30 is 15. Therefore, a half of 230 is 115. This means that Simon can buy another five gobstoppers at 23 credits for a total of 115 credits.

23 multiplied by two is equal to 46, as 20 multiplied by two is 40 and three multiplied by two is equal to six. Simon can get an extra two gobstoppers for 46 credits. Adding 230, 115, and 46 gives us 391. This means that Simon can buy 17 gobstoppers for 391 credits. As each gobstopper was worth 23 credits, he doesn’t have enough to buy an extra gobstopper.

We have worked out that 17 multiplied by 23 is equal to 391 credits. Currently, Simon has 20 cola bottles and he has 17 gobstoppers. We now need to consider the change or the remainder from the calculation 400 divided by 23. Simon used 391 credits to buy gobstoppers. This means that 400 divided by 23 is equal to 17, remainder nine. He has used 391 of the 400 credits so has nine remaining.

We are told that Simon uses these extra credits to buy more cola bottles. Well, each cola bottle is worth five credits. So to buy two cola bottles, Simon would need 10 credits. As Simon only has nine credits remaining, he can only buy one extra cola bottle. One extra cola bottle would use an additional five credits.

We can therefore see that, altogether, Simon buys 21 cola bottles and 17 gobstoppers. He does have four credits remaining. But this is not enough to buy an extra cola bottle or gobstopper.

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