Video: GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 11

GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 11

04:47

Video Transcript

The graph below can be used to convert between pounds and kilograms. Part a) Write down 44 kilograms in pounds. Paulina buys a new fridge. The weight of the fridge is 17 stone and 12 pounds. Part b) Given that one stone is equal to 14 pounds, work out the weight of Paulina’s fridge in kilograms.

Our first step when dealing with a graph like this is to work out what each little square represents on the 𝑥- and the 𝑦-axis. On the 𝑥-axis, 10 squares represent 10 kilograms. Dividing both sides of this by 10 tells us that one square is equal to one kilogram. On the 𝑦-axis, 10 little squares is equal to 20 pounds. Dividing both sides of this by 10 tells us that one square is equal to two pounds on the 𝑦-axis, as 20 divided by 10 is equal to two.

The first part of our question asked us to convert 44 kilograms into pounds. We draw a vertical line up from 44 until we hit our graph. We then draw a horizontal line across to the 𝑦-axis. This line is one and a half squares below 100. Therefore, 44 kilograms is equal to 97 pounds. One and a half squares on the 𝑦-axis would be equal to three pounds, and 100 minus three is equal to 97.

It is important to note that, in an exam, there will be a small margin for error in this type of question. However, we need to be as accurate as we possibly can be. It’s often recommended to draw lines in pencil first in case we make a mistake.

The second part of our question told us that Paulina bought a fridge that weighed 17 stone and 12 pounds. As one stone is equal to 14 pounds, then 17 stone would be equal to 17 multiplied by 14 pounds. 17 multiplied by 14 is equal to 238. Therefore, 17 stone is equal to 238 pounds. This means that 17 stone and 12 pounds is equal to 250 pounds, as 238 plus 12 is equal to 250.

Our next step is to try and find 250 pounds on the 𝑦-axis. Unfortunately, our scale only goes up to 140. This means that we need to find a factor of 250 and then we can scale up our answer. One-half of 250 is 125. Therefore, we need to draw a horizontal line from 125 pounds.

Note that 125 is two and a half squares above 120. Drawing a line vertically down from this point gives us 56.5 kilograms. This is because the line is halfway between the sixth and seventh square after 50. We can therefore say that 125 pounds is equal to 56.5 kilograms. As 250 is double 125, we need to multiply both sides of this equation by two. 250 pounds is equal to 113 kilograms, as 56.5 multiplied by two is equal to 113. We can therefore say that Paulina’s fridge that weighed 17 stone and 12 pounds is also equal to 113 kilograms.

Using a conversion graph is a good way to convert between metric and imperial units. Kilograms are metric, and pounds are imperial. In many exams, we’re also expected to know that 2.2 pounds is equal to one kilogram. This can be shown from the graph, as 22 pounds is equal to 10 kilograms. And dividing both of these numbers by 10 gives us 2.2 pounds is equal to one kilogram.

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