Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 19

GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 19

03:36

Video Transcript

A factory makes cups, bottles, and buckets. The factory makes 275 of these items in one day. 146 of the items are cups, which hold 200 millilitres of water. Two-fifths of the items are bottles, which hold 500 millilitres of water. The rest of the items are buckets, which hold 2.5 litres of water. One litre is equal to 1000 millilitres. What is the total volume of water in litres needed to fill all 275 items?

Let’s begin by calculating the number of items which are bottles and buckets. We are told that two-fifths of the items are bottles. To find two-fifths of a number, we first find one-fifth. And to find a fifth of 275, we divide 275 by five.

We can use the bus stop method to do this. We can’t do two divided by five, so instead we divide 27 by five. 27 divided by five is five with a remainder of two. Then 25 divided by five is five. This means that one-fifth of 275 is 55.

To find two-fifths of the number, we multiply the value of one-fifth by two. 55 multiplied by two is 110, so there are 110 bottles. We can then find the number of items which are buckets by subtracting the number of items that are cups and the number of items that are bottles from the total that was 275. There are 146 cups and 110 bottles. 146 plus 110 is 256. 275 minus 256 is 19. So there are 19 buckets.

We want to find the total volume required, so let’s find the volume required to fill each of the cups, the bottles, and buckets. There are 146 cups, each of which holds 200 millilitres of water. We can multiply then 146 by 200 to get the total volume of water required to fill the cups as 29200 millilitres.

Remember though, our answer needs to be in litres, and we know that one litre is equal to 1000 millilitres. We can therefore divide this by 1000, and that tells us that the total volume of water required to fill the cups is 29.2 litres.

110 of the items are bottles, and they each hold 500 millilitres of water. 110 multiplied by 500 is 55000 millilitres. That means that the bottles hold a total of 55 litres. There are 19 buckets, and we already know that they hold 2.5 litres of water. 19 multiplied by 2.5 is 47.5 litres. We don’t need to do any conversions here because these measurements are already in litres.

To get the total volume of water required to fill the items, we’re going to add these three numbers. 29.2 plus 55 plus 47.5 is 131.7. The total volume of water required is 131.7 litres.

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