Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 6

GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 6

06:34

Video Transcript

Milk is sold in bottles. Each bottle contains 500 milliliters of milk. Shaun eats one bowl of cereal and drinks three cups of tea each day. He thinks that he uses 150 milliliters of milk in each bowl of cereal and 10 milliliters of milk in each cup of tea. Shaun wants to buy enough milk to last him one week. Part a) How many bottles of milk does Shaun need to buy?

We’ll also deal with the rest of the question in a bit. So what we want to do is actually see how many bottles of milk that Shaun needs to buy. So we want to first of all see how much milk he actually uses. And we know that it’s for one week, because he wants to buy enough milk to last him that week.

So Shaun eats one bowl of cereal, and he thinks that he uses 150 milliliters of milk in each bowl of cereal. So therefore, what we’re gonna do is actually multiply 150, because it’s 150 milliliters, cause we said he has one bowl of cereal and each one uses 150 milliliters and that’s per day. But we want to find out how much it is for the whole week, so that’s why we multiply it by seven, because there are seven days in a week. And this is equal to 1050 milliliters. So we can say that’s the amount of milk that he uses in his cereal for a week.

So now we’ve dealt with the cereal, we can move on to the tea. And we see that Shaun drinks three cups of tea each day, and he thinks that he uses 10 milliliters of milk per cup. So then to work out the amount of milk he uses in his tea for the week, we’re gonna do 10 multiplied by three. That’s cause we have 10 milliliters of milk in each cup and there are three cups a day. Then we’re gonna multiply this by seven, because there are seven days in a week, which is gonna give us a total amount of milk used in tea for the week as 210 milliliters.

So therefore, we can now calculate the total milk used in a week, cause it’s gonna be 1050, because that was the total milk he used for cereal, plus 210, because that was the total milk used for tea. That gives us a total amount of milk of 1260 milliliters used for the week. So that’s what Shaun is gonna use for his week. So he wants to buy enough milk to last him one week. But how are we going to work that out?

Well, we’re told that milk is sold in bottles, and each bottle contains 500 milliliters of milk. So therefore, we know that one bottle is equal to 500 milliliters like I said. And therefore, if we bought two bottles, this will be equal to 1000 milliliters, because it’ll be 500 add 500. But this still isn’t enough milk, cause he needs 1260 milliliters. But if he bought three bottles, this will be equal to 1500 milliliters. And we can see that 1500 is actually bigger than 1260, so we’d have enough milk to deal with his cereal and tea needs. So therefore, we can say that Shaun will need to buy three bottles of milk.

Okay, great! Now let’s move on to part b). So for part b), we’ve got a bit of extra information. Shaun later finds that he uses 155 milliliters of milk in each bowl of cereal and 15 milliliters of milk in each cup of tea. Part b) How does this affect how many bottles of milk Shaun needs to buy? You must justify your answer.

So in order to actually solve this problem, what we need to do actually first of all is find out how much extra milk Shaun’s actually going to use. So we can start with cereal. And we can work out the amount of extra milk that he needs to use by first of all subtracting 150, because that was the amount he thought he used, from 155, which is the amount he now knows that he uses. So therefore, we can see that he’s gonna use five milliliters extra milk per day on his cereal.

But Shaun wants to actually buy the milk for the whole week. So what we need to do is actually find out how much extra this will be per week. And to do that, we’re gonna multiply the five from our five milliliters per day by seven, the number of days in the week. And when we do that, we get 35 milliliters. So that’s great. We know the extra milk needed for cereal over the whole week is 35 milliliters.

So now we can actually move on to tea. And we know that, originally, Shaun thought that he used 10 milliliters of milk in each cup of tea. However, we now know that he uses 15 milliliters of milk in each cup of tea. So therefore, we’re gonna do 15 minus 10, which is gonna give us five. So we know that he uses five milliliters per cup more.

So therefore, if we wanna work out the total extra milk used for tea per day, we have to do five multiplied by three, cause it’s five milliliters extra per cup and he has three cups of tea per day, which is gonna be equal to 15 milliliters per day extra milk in his tea.

So again, obviously, we want to find out how much it’s going to be per week and that’s only per day. So therefore, what we’re gonna do is 15 multiplied by seven, and that’s cause it’s 15 milliliters per day and we have seven days in a week. So this will give us 105 milliliters of extra milk for tea in the week.

So now that we’ve got the extra milk used, what we can do is actually work out the total milk used now for Shaun in the whole week if he counts for his tea and his cereal. And his total milk used is going to be equal to 1260, because that was the original amount that we calculated for part a), plus 105, because that’s the extra milk he needs for tea, plus 35, because that’s the extra milk he now needs for cereal. And this equals 1400 milliliters or one thousand four hundred milliliters of total milk used now by Shaun.

Okay, but does this answer the question? Well, the answer is no, because what the question wants us to do is actually work out how does this affect how many bottles of milk Shaun needs to buy. So we’ve increased it now to 1400 milliliters. Will this have an effect?

Well, if we look back at part a), we can remind ourselves that actually he was gonna buy three bottles of milk, and we also know that each bottle is 500 milliliters. So therefore, if we can work out the total amount of milk that he was gonna buy, it’s gonna be three multiplied by 500, which is actually equal to 1500 milliliters. Well, 1500 or one thousand five hundred milliliters is greater than 1400 milliliters, and that’s the amount of total milk used even with the extra.

So therefore, three bottles of milk is going to be enough. So therefore, we can conclude that actually there’s going to be no effect to the number of bottles of milk that Shaun needs to buy, because the number of bottles doesn’t change as Shaun will have enough milk already.

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