Video: KS2-M16 • Paper 2 • Question 9

The cost of 6 pencils is £1.68. The cost of 3 pencils and 1 rubber is £1.09. What is the cost of 1 rubber?

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Video Transcript

The cost of six pencils is one pound 68. The cost of three pencils and one rubber is one pound nine. What is the cost of one rubber?

In this problem, we’re asked to find the cost of one rubber. This is the sort of problem where we need to ask ourself two questions. We might not know what the cost of one rubber is. But what do we know and how can we use it to help? First of all, what do we know? Firstly, we know how much six pencils cost. How could we use this to help? Well, we could use this fact to help us work out what one pencil costs or even how much three pencils cost. We’re also told the cost of three pencils and a rubber. How can we use this to help?

Well, if we’ve already worked out the cost of three pencils, we can take this away from one pound and nine. And this should leave us with the cost of one rubber. Let’s go through each step now to find the answer. We can start by using the first fact to find the cost of three pencils. Six pencils cost one pound 68. Because it is written as a decimal number, it might be easier to convert it into pence. One pound 68 is the same as 168 pence. If six pencils cost 168 pence, how can we work out the cost of three pencils?

Well, three is half of six. So we’d expect the cost of three pencils to be half the cost of six pencils, or half of 168 pence. What’s a quick way to find half of 168? Well, we could use written division. But it might be quicker just to work out the answer in our heads. We can think of 168 as 100 and 68. Half of 100 is 50. Half of 68 is 34. And so, half of 168 is 50 plus 34, which is 84. So we know now that three pencils cost 84 pence. How can we use this to help?

Well, we know that the cost of three pencils and a rubber is one pound nine or 109 pence. So all we need to do is to subtract 84 from 109 to find the answer. How can we do this quickly? Well, 84 is quite near to 109. So we could start with 84 and count on. 84 is 16 away from 100. And then, if we count on another nine, we get to 109. 16 and nine is 25. And so the cost of one rubber is 25 pence.

We found the answer by starting with the cost of six pencils. We thought that finding the cost of three pencils would help. So we converted the price in pounds into pence and then we halved it. This gave us the price for three pencils. Once we’d worked out the price for three pencils, we wanted to subtract this from the cost of three pencils and one rubber. So again, we converted from pounds into pence, just to make things easier. And then we did a mental subtraction. We took away the cost of three pencils. And we were left with the cost of one rubber.

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