Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 2 • Question 20

A farm is home to some owls and some mice. The total number of mice is between 40 and 60. The ratio of owls to mice is 4 : 17. How many owls and mice are on the farm altogether?

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Video Transcript

A farm is home to some owls and some mice. The total number of mice is between 40 and 60. The ratio of owls to mice is 4 : 17. How many owls and mice are on the farm altogether?

We’re told in the question that the ratio of owls to mice is four to 17. This means that, for every four owls, there are 17 mice. We can scale this ratio up by multiplying both numbers by the same number. If we multiply both sides of the ratio by two, we get the ratio eight to 34 as two multiplied by four is equal to eight. And two multiplied by 17 is 34.

We were also told in the question that the total number of mice is between 40 and 60. Therefore, 34 mice is too small. Multiplying the ratio four to 17 by three gives us the ratio 12 to 51. 51 is between 40 and 60. Therefore, this appears to be the correct answer.

We can check this by multiplying both sides of the initial ratio by four. Four multiplied by four is equal to 16. And 17 multiplied by four is equal to 68. This time, the number of mice is too large as 68 is greater than 60. As the ratio of owls to mice is four to 17 and the number of mice is between 40 and 60, there must be 12 owls and 51 mice on the farm.

We were asked to work out how many owls and mice are on the farm altogether. Therefore, we need to add 12 and 51. 12 plus 51 is equal to 63. Therefore, there are 63 owls and mice on the farm.

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