Video: Pack 4 • Paper 1 • Question 5

Pack 4 • Paper 1 • Question 5

03:41

Video Transcript

The diagram shows a plastic container which is in the shape of a cuboid. David wants to fill the container with custard. One pot of custard contains 125 milliliters of custard and costs three pounds 50. David says, “It will cost at least 21 pounds to fill the container with custard.” Is David right? Justify your answer.

To answer this question, we first need to calculate the volume of the plastic container. To find the volume of a cuboid, we multiply its length by its width by its height. So that’s 20 multiplied by 10 multiplied by four. The volume of the container is, therefore, 800 centimeters cubed.

We need to work out how many pots of custard are needed to fill this container. And we know that each pot contains 125 milliliters of custard. We, therefore, need to know how to convert the volume of 800 centimeters cubed into a capacity in milliliters. This is actually quite straightforward as it’s a one-to-one conversion. One centimeter cubed of volume can contain one milliliter of liquid. Therefore, to fill the volume of 800 centimeters cubed in this plastic container, we’re going to need 800 milliliters of custard.

Now, let’s work out how many pots that’s equivalent to. We need to work out how many times 125 goes into 800. So that’s 800 divided by 125. This fraction can be simplified as both 800 and 125 can be divided by 25. 125 divided by 25 is five and 800 divided by 25 is 32 as there are four lots of 25 in each 100. And four multiplied by eight is 32. So we have 32 over five. As a mixed number, this is six and two-fifths as six fives are 30 and two-fifths as a decimal is 0.4. So 32 divided by five is 6.4.

This number is a decimal. And of course, you can’t go into a shop and ask to buy 6.4 pots of custard. So we need to round it. And we need to round this number up. Normally, 6.4 will be rounded down to six. But six pots of custard won’t be enough. So we have to round it up to seven.

Next, we need to work out the cost of buying these seven pots of custard. And as each pot costs three pound 50, our calculation is three pound 50 multiplied by seven. We can do this using a column method. And as only one of the numbers that we’re multiplying is a decimal, the decimal point in the answer will go directly below the decimal point in the question.

Working from the right, zero multiplied by seven is zero and five multiplied by seven is 35. Three multiplied by seven is 21. And adding the three that we’ve carried over into this column, we have 24.50. The total cost of buying these seven pots of custard is, therefore, 24 pounds 50.

Let’s return to David’s statement. Well, he says that it will cost at least 21 pounds to fill the container with custard. Is David right? Yes, he is. He needs to buy seven pots, which we’ve shown will cost 24 pounds 50 which is more than 21 pounds. Remember David doesn’t need all of the last pot. So he will have some custard left over. But he has to buy the seven pots in order to have enough to fill the container.

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