Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 8

GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 8

03:30

Video Transcript

Data Saver is a data backup service. The graph below shows the monthly cost of backing up data per gigabyte. The service includes backing up eight gigabytes of data for free and then a charge for each extra one gigabyte. Work out the charge for backing up each one gigabyte of data beyond the initial free eight gigabytes.

So looking at the graph that we’ve been given, we can see that we have the number of gigabytes of data backed up on the horizontal axis and then the cost of backing up that data in euros on the vertical axis. We’re told in the question that the service includes backing up eight gigabytes of data for free, which is why the line only starts at eight on the horizontal axis.

To work out the charge for backing up each one gigabyte of data beyond this initial free amount, we need to find the cost of backing up a certain amount of data. So we need to find one point that is on this line. In order to be as accurate as possible, we’ll want to choose a point where the line goes exactly through the corner of the small squares, so we’ll choose this point here.

If we read vertically down to the horizontal axis, we can see that this point corresponds to backing up 40 gigabytes of data. If we look horizontally across to the vertical axis, we can see that this point has a value that is one small square below 15 on the vertical axis. So we need to be clear what the scale of this axis is. If we look closely, we can see that five small squares represents five euros. So dividing by five, we see then that one small square represents one euro, so each small square on the vertical axis is one euro. So one small square below 15 then means 14, and we found that, for 40 gigabytes of data, we’ll pay 14 euros.

But remember, we actually don’t pay for the first eight gigabytes of data. They’re free. So instead of 40 gigabytes of data costing 14 euros, it’s actually 32 gigabytes of data that cost 14 euros. To find the cost of each gigabyte of data then, we need to divide by 32. 14 divided by 32 is 0.4375. So this tells us that each gigabyte of data costs 0.4375 euros.

However, it makes sense to round our answer. And as we’re dealing with money, we’ll round to two decimal places, giving a value of 0.44 euros. So we can conclude then that, beyond the initial free eight gigabytes, the charge for backing up each gigabyte of data is 0.44 euros.

Now this is an approximate answer, firstly because we had to round it to two decimal places and secondly because we had to read values off our graph in order to work this out. If we’d chosen a different point on the graph, we may have got a slightly different answer. In reality then, there’ll probably be an acceptable range of values in which your answer can lie, perhaps from 0.42 to 0.46 euros. There isn’t a huge margin for error though, so you do need to be as accurate as possible when reading values from the graph.

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