### Video Transcript

A boy was reading a book and found out that, after reading for two hours, he still had 344 pages left and, after reading for three hours, he had 43 pages left to read. Find the linear equation between the time 𝑡 and the number of pages left to read 𝑏.

So first of all, we look back at the question to see what information we have. And we know that, after reading for two hours, he had 344 pages left. And after three hours, he had 43 pages left. So therefore, we can actually use this to help us work out how many pages he read in an hour. In order to use that information to actually find out how much he reads in an hour, we have to actually make an assumption. And we’re making that assumption because we know that it’s a linear equation that can be found as a relationship between 𝑡 and 𝑏. And the assumption we’re making is that he reads at a constant speed.

So therefore, we can work out the pages read in an hour by taking 43 away from 344. And that’s because after two hours, he had 344 pages left. And as we said, after three hours, he had 43 pages left. There is an hour between them. So, I’ve set it up as a column subtraction. So, we got four take away three, which gives us one. Then, four take away four or 40 take away 40 is zero. And then three take away zero just gives us three. So, we’ve got 301. So, in that case, we know that the boy reads 301 pages in an hour.

So next, what we want to do is actually work out what the total number of pages in the book. And to work out the total number of pages in the book, it’s gonna be equal to 344 — because that, as we said, was the pages left after two hours — plus then two multiplied by 301. And that’s because he’d been reading for two hours, and we know that he reads 301 pages per hour. So, this is gonna be equal to 344 plus 602. Again, I’ve set it up as a column addition. So then, we’ve got four plus two is six, four plus zero is four, and three plus six is nine. So, we got 946. So, we know there are 946 pages in the book.

So therefore, we’ve got the two bits of information that we need to actually formulate our equation. So therefore, we can say that 𝑏, which is the number of pages left to read, is gonna to be equal to 946, because this is our total number of pages, then minus 301 multiplied by 𝑡. And this is because it’s the total number of pages minus the number of hours that he’s actually read, which is 𝑡, multiplied by 301, because we know that’s how many pages he reads in an hour. And we can actually rewrite it as 𝑏 equals negative 301𝑡 plus 946.

So therefore, we can say that if a boy was reading a book and found out that, after reading for two hours, he still had 344 pages left. And after reading for three hours, he had 43 pages left to read. Then, the linear equation that connects 𝑡, time, and 𝑏, the number of pages left to read, is 𝑏 is equal to negative 301𝑡 plus 946. And this is making the assumption that he reads at a constant speed.