### 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.

Thereโs also a second part to the question that weโll come on too. So if weโre 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 thatโs because what weโre 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 isnโt involved with the fraction of ๐ first. So weโre 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, weโre gonna get seven multiplied by ๐ minus 10 equals ๐ minus 40. And then finally, what weโre 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; thatโs 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 weโre 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 weโve got. And a piece of information we have is that ๐ is equal to 22. Thatโs 22 degrees Celsius. Now, that means that we have the other missing variable in our formula because ๐ is what weโre 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 weโre gonna get is ๐ is equal to seven multiplied by, then weโve 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, weโre gonna get ๐ is equal to 124. So weโve 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 youโd expect here in a minute is 124.