Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 3 • Question 13

The scale of a model car is 1 : 24. The length of the model car is 180 mm. Calculate the length of the original car in metres.

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Video Transcript

The scale of a model car is one to 24. The length of the model car is 180 millimetres. Calculate the length of the original car in metres.

We’re told that the scale or ratio is one to 24. This means that for every one unit on the model, we have 24 units on the original car. As the length of the model car is 180 millimetres, we need to multiply 24 by 180 to calculate the length of the original car in millimetres. 24 multiplied by 180 is 4320. This means that the length of the original car in millimetres is 4320.

We know that 10 millimetres is equal to one centimetre. We also know from one of our standard conversions that 100 centimetres is equal to one metre. 10 multiplied by 100 is equal to 1000. Therefore, there are 1000 millimetres in one metre. To calculate the length of the original car in metres, we need to divide 4320 by 1000. Dividing by 1000 moves all of the digits three places to the right. This means that 4320 divided by 1000 is equal to 4.32. We can therefore say that the length of the original car in metres is 4.32. This seems a sensible answer for the length of a car.

If the decimal point had been between the three and the two, we would have an answer of 43.2 metres. This is far too big and is unrealistic for the length of a car. In the same way, 0.432 metres would be too small and again would be unrealistic.

If the length of a model car is 180 millimetres and the scale is one to 24, then the length of the original car is 4.32 metres.

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