Video: Changing the Subject of a Formula

In 1897, Amos Dolbear derived a formula linking the number of cricket chirps and the temperature. The law states that the temperature ๐‘‡, in degrees Celsius, is related to the number of cricket chirps in a minute ๐‘ by the formula ๐‘‡ = 10 + ((๐‘ โˆ’ 40)/7). Rearrange the formula to make ๐‘ the subject. Given that the temperature on a particular day is 22ยฐC, estimate the number of cricket chirps that you would expect to hear in a minute.

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Video Transcript

In 1897, Amos Dolbear derived a formula linking the number of cricket chirps and the temperature. The law states that the temperature ๐‘‡, in degrees Celsius, is related to the number of cricket chirps in a minute ๐‘ by the formula ๐‘‡ equals 10 plus ๐‘ minus 40 over seven. Rearrange the formula to make ๐‘ the subject.

Thereโ€™s also a second part to the question that weโ€™ll come on too. So if weโ€™re looking to rearrange this formula to make ๐‘ the subject, what want to do is we want to complete inverse operations. Well, the first thing we want to do is we want to subtract 10 from each side of the equation. And thatโ€™s because what weโ€™re trying to have is ๐‘ the subject, so ๐‘ on its own on the right-hand side. So we always deal with the part that isnโ€™t involved with the fraction of ๐‘ first. So weโ€™re going to subtract 10 from each side. So when we do that, we get ๐‘‡ minus 10 equals ๐‘ minus 40 over seven.

So next, what we want to do is multiply both sides of the equation by seven. So when we do this, weโ€™re gonna get seven multiplied by ๐‘‡ minus 10 equals ๐‘ minus 40. And then finally, what weโ€™re gonna do is we gonna add 40 to each side of the equation. So this is gonna leave us with seven multiplied by ๐‘‡ minus 10 plus 40 is equal to ๐‘. Now, we can leave it like this; thatโ€™s totally fine. If we wanted to, we could also distribute across the parentheses. But this form is fine for this question. So now, what we can do is weโ€™re gonna move to the second part of the question.

Now, part two gets us to use our formula because it says, given that the temperature on a particular day is 22 degrees Celsius, estimate the number of cricket chirps that you would expect to hear in a minute.

Well, straight away, we can find out what information weโ€™ve got. And a piece of information we have is that ๐‘‡ is equal to 22. Thatโ€™s 22 degrees Celsius. Now, that means that we have the other missing variable in our formula because ๐‘ is what weโ€™re looking for. And we know ๐‘‡. So now, we can substitute this in to find out what ๐‘ is going to be. So when we do that substituting, what weโ€™re gonna get is ๐‘ is equal to seven multiplied by, then weโ€™ve got 22 minus 10 because ๐‘‡ was equal to 22, then plus 40. So this is gonna give us ๐‘ is equal to seven multiplied by 12 plus 40. So therefore, weโ€™re gonna get ๐‘ is equal to 124. So weโ€™ve reached the final answer.

So first of all, we can say that if we rearrange our formula, the new formula with ๐‘ is the subject is gonna be ๐‘ is equal to seven multiplied by ๐‘‡ minus 10 plus 40. And also, if the temperature on a particular day is 22 degrees Celsius, then the number of cricket chirps youโ€™d expect here in a minute is 124.

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