Systems of equations word problems
We're told that in 40 years, Imran will be 11 times as old as he is right now. And then we're asked, how old is he right now? And so I encourage you to try this on your own. Well, let's see if we can set this up as an equation. So let's figure out what our unknown is first. Well, our unknown is how old he is right now. I'm just arbitrarily using x. We always like to use x. But I could've really set it to be anything. But let's say x is equal to how old he is right now. How old-- not how hold. How old he is now. Now, what do we know about how old he will be in 40 years? Well, he's going to be how old he is now plus 40. So let me write that down. So in 40 years Imran is going to be x plus 40, plus this 40 right over here. But they give us another piece of information. This by itself isn't enough to figure out how old he is right now. But they tell us in 40 years, Imran will be 11 times as old as he is right now. So that's saying that this quantity right over here, x plus 40, is going to be 11 times x. In 40 years, he's going to be 11 times as old as he is right now. So this is going to be times 11. You take x, multiply it times 11, you're going to get how old he's going to be in 40 years. So let's write that down as an equation. You take x, multiply it by 11, so 11 times as old as he is right now is how old he is going to be in 40 years. And we have set up a nice little, tidy linear equation now. So we just have to solve for x. So let's get all the x's on the left-hand side. We have more x's here than on the right-hand side. So we avoid negative numbers, let's stick all the x's here. So if I want to get rid of this x on the right hand side, I'd want to subtract an x. But obviously, I can't just do it to the right. Otherwise, the equality won't be true anymore. I need to do it on the left as well. And so I am left with-- if I have 11 of something and I take away 1 of them, I'm left with 10 of that something. So I'm left with 10 times x is equal to-- well, these x's, x minus x is just 0. That was the whole point. It's going to be equal to 40. And you could do this in your head at this point, but let's just solve it formally. So if we want a 1 coefficient here, we'd want to divide by 10, but we've got to do that to both sides. And so we are left with-- and we could have our drum roll now. We are left with x is equal to 4 years old. x is equal to 4. So our answer to the question, how old is Imran right now? He is 4 years old. And let's verify this. If he's 4 years old right now, in 40 years he's going to be 44 years old. And 44 years old is indeed 11 times older than 4 years old. This is a factor of 11 years, so it all worked out.