Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 3 • Question 7

(a) A wedding cake has a mass of 5 kilograms to the nearest kilogram. Fill in the error interval for the mass of the wedding cake. (b) The mass of another wedding cake is 3 kilograms to the nearest kilogram. David weighs the two wedding cakes and says, “Their total mass is seven kilograms to the nearest kilogram.” Give an example to show that David could be correct.

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Video Transcript

Part a) A wedding cake has a mass of five kilograms to the nearest kilogram. Fill in the error interval for the mass of the wedding cake. Part b) The mass of another wedding cake is three kilograms to the nearest kilogram. David weighs the two wedding cakes and says their total mass is seven kilograms to the nearest kilogram. Give an example to show that David could be correct.

So from part a, we can see that a wedding cake has a mass of five kilograms to the nearest kilogram. So therefore, if we take a look at the number line that I’ve drawn, we can see that the possible values for the mass of the wedding cake are between 4.5 and 5.5, because we can see that anything from 4.5 kilograms, including 4.5 kilograms, up to five kilograms would round up to five kilograms and anything from 5.5 kilograms but not including 5.5 kilograms would round down to five kilograms. And that’s the reason we have an open circle or open dot above 5.5 and a closed circle or closed dot above 4.5, because the closed dot means it includes that value. The open dot means it does not include that value.

So therefore, we can say that the mass of the wedding cake is gonna be greater than or equal to 4.5 kilograms but less than 5.5 kilograms. And we can show that using an error interval, which is what I’ve done here in the green box. So we’ve got an open bracket and then we have 4.5 and then we have less than or equal to. And that’s or equal to cause it’s got the line underneath. And then we’ve got the mass and we’ve got less than 5.5. And I’m gonna close our brackets. That’s kilograms.

So again, that’s telling us that the mass is greater than or equal to 4.5 kilograms but less than 5.5 kilograms. And we’ve now filled in the error interval to show that the mass of a five-kilogram cake to the nearest kilogram this is its possible error interval. Right, now we can move on to part b. And what we need to do in part b is give an example to show that if we have a mass of one wedding cake at three kilograms to the nearest kilogram and then a mass of another wedding cake at five kilograms to the nearest kilogram, their total mass could be seven kilograms to the nearest kilogram.

So again, what I’ve done is I’ve drawn a number line to help us solve this problem. So our number line shows the total mass being seven kilograms to the nearest kilogram. So therefore, the values of the total mass are greater than or equal to 6.5 kilograms — again, that’s why I’ve got the colored in dot above that — but less than 7.5 kilograms. And again, it’s because from 6.5 to seven would round up to seven kilograms. And from 7.5 down to seven would round down to seven kilograms, remembering not include our seven and a half or 7.5 kilograms.

So what we now need to do is see that when we add together the weights of the other two cakes, it’s gonna be somewhere in between this interval. So I’ve drawn another number line. And this is for the wedding cake that is three kilograms to the nearest kilogram. And here I’ve shown that it’s gonna be greater than or equal to 2.5 but less than 3.5.

Well, in fact, there’ll be a number of combinations for the weights of each cake. And we’d generally be looking in the areas from 4.5 to five kilograms for the first cake and 2.5 to three kilograms for the second cake. In this problem, we’re just asked to pick an example though. So I’m gonna pick one example that will work, that comes from this region.

Well, I’m gonna choose cake one being equal to 4.5 kilograms because we’ve already shown that that would round up to five kilograms so that would work, and cake two being equal to 2.5 kilograms. Again, that would round up to three kilograms so that’d work for the weight of the second cake. And if we add these together, we’d get 4.5 plus 2.5. We can do it in a column addition.

So first, we would have five add five, which will be 10. So I put a zero in the column there, which would be the first decimal, so our tenths column, and carry our one into the units column. And then we have four add two add the one we carried gives us seven. So we’ve got seven kilograms. So this gives us seven kilograms, which is a total mass of seven kilograms to the nearest kilogram.

As I said, there are other values that you could choose. And you could choose values, for instance, such as 4.5 and 2.6 or 4.5 and 2.8. And there will also be other values for the first wedding cake. You could use that 4.6, add it to a different value, say 2.5, from the second cake. So there are lots of different combinations, but this is one combination. So I’ve given an example to show that David could be correct.

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