Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 3 • Question 6

Jeremy is in charge of a factory which produces soap. He records the amount of water used in the factory each day. Every day, 133 litres of water is used to clean the machines. The rest of the water is used to produce soap. a) Work out the amount of water used to produce soap on Wednesday. b) The amount of water used in the factory on Tuesday is double the amount of water used in the factory on Friday. Jeremy says “The amount of water used to make soap on Tuesday is double the amount of water used to make soap on Friday.” Is Jeremy correct? You must show your working.

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Video Transcript

Jeremy is in charge of a factory which produces soap. He records the amount of water used in the factory each day. Every day, 133 litres of water is used to clean the machines. The rest of the water is used to produce soap. Part a) Work out the amount of water used to produce soap on Wednesday. There’s also a part b) that we will look at later.

Before starting any question like this, it is important to understand what the graph shows. In this case, it is showing the volume of water in litres that was used on Monday, Tuesday, Wednesday, Thursday, and Friday. The five crosses represent the volume of water used on that day. The lines joining each point tell us whether the volume of water was increasing or decreasing from day to day. As the line slopes downwards from Monday to Tuesday, there was less water used on Tuesday than on Monday. In the same way, the line from Tuesday to Wednesday slopes upwards. This means there was more water used on Wednesday than on Tuesday.

It is also important to understand what each line or square on the axis represents. On the 𝑦-axis, four squares represent 200 litres of water. This means that one square or each square represents 50 litres of water as 200 divided by four is equal to 50. The cross or point for Monday is one square above 1800. Adding 50 to 1800 gives us 1850. This is the volume of water in litres that was used on Monday.

The point for Tuesday is halfway between 1200 and 1400. It is two squares above 1200 and two squares below 1400. Therefore, 1300 litres of water was used on Tuesday. The volume of water used on Wednesday was 1600 litres. On Thursday, it was 750 litres. And on Friday, it was 650 litres. We’re also told in the question that, on every day, 133 litres of water is used to clean the machines. The rest of the water is used to produce soap.

In the first part of the question, we are asked to work out the amount of water that was used to produce soap on Wednesday. On Wednesday, there was a total of 1600 litres used. We know that 133 litres was used to clean the machines. Therefore, we need to subtract 133 from 1600. This is equal to 1467 litres. The amount of water that was used to produce soap in the factory on Wednesday is 1467 litres.

We could also work out the amount of water used to produce soap on the other days by subtracting 133 from the total. 1850 minus 133 is equal to 1717. Subtracting 133 from 1300, 750, and 650 gives us answers of 1167, 617, and 517, respectively. The volume of water in litres that was used to produce soap from Monday to Friday was 1717, 1167, 1467, 617, and finally 517. The second part of the question says the following.

b) The amount of water used in the factory on Tuesday is double the amount of water used in the factory on Friday. Jeremy says “The amount of water used to make soap on Tuesday is double the amount of water used to make soap on Friday.” Is Jeremy correct? You must show your working.

In this question, we are comparing what happened on Tuesday with what happened on Friday. The first sentence tells us that the total amount of water on Tuesday is double the total amount of water on Friday. This is because 1300 is equal to two multiplied by 650. 1300 is double 650. The amount of water used to clean the machines is constant, 133 litres on each day. As we have already calculated, the amount of water used to make soap on Tuesday is 1167 litres. We did this by subtracting 133 from 1300. On Friday, the amount of water used to make soap was 517 litres as 650 minus 133 is 517. 517 multiplied by two is equal to 1034. 1034 is not equal to 1167.

We can therefore conclude that Jeremy was not correct. The amount of water used to make soap on Tuesday was not double the amount of water used to make soap on Friday. In fact, it was more than double as 1167 is greater than 1034.

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