Transcription
Welcome to the second set of presentations on age word problems. I have one typed out here. Let's see what it says. It says, Salman—that's me—is 108 years old. And so this is clearly at some vast time in the future. And this'll only happen if my caloric restriction works out. But Salman is 108 years old. Jonathan is 24 years old. How many years will it take for Salman to be exactly 4 times as old as Jonathan?
Well, let's figure this one out. What we're trying to solve for is how many years will it take. So let's use the variable y, for years. So y equals years until, let's just say Sal, for short. Sal is 4 times Jonathan's age. Well, if today, I, or Sal, if Salman, it's hard to speak in the third person. If Salman is 100 years old today, in y years, Salman will be 108 plus y is equal to Sal in y years. We'll say y years. Sal in y years is going to be 108 plus y. And then Jonathan in y years, that's pretty easy. He's going to be 24 plus y. So that's, I'll say Jon for short. In y years. Not years. y years.
And what else does the problem say? It says, in how many years would take for Salman to be exactly—I should put that in another color for emphasis—exactly 4 times as old as Jonathan? Well, and the exactly is important. Because Salman is already more than 4 times as old as Jonathan. But they want to figure out exactly when is Salman going to be 4 times as old as Jonathan. Well, in y years Salman is going to be 108 plus y. So we know that. 108 plus y. And after y years, he's going to be 4 times as old as Jonathan. Exactly 4 times. And Jonathan's going to be 24 plus y years old. And now we just solve the equation. Get 108 plus y is equal to 4 times 24. Well, 4 times 25 is 100. And we can subtract 4 from there. So it's 96. Plus 4y. And now we just solve this equation. We get 3. 3, I'm going to skip some steps, because I think this part is easy for you. 3y will equal 108 minus 96. So we get 3y is equal to, what is that, 12, right? So y is equal to 4. So our algebra has told us that in 4 years Salman is going to be exactly 4 times as old as Jonathan.
Let's see if that's true. Well, if Salman is 108 right now, in 4 years he's going to be 112. And if Jonathan is 24 right now, in 4 years he's going to be 28. And let's see. 28 times 4 is 80 plus 32. Yep, exactly. He'll be 112. Looks like that problem worked. Excellent. Let's do another one. Hope you didn't hear that, it was my stomach growling. See how hard I work on this site? Don't even eat properly. Let's do another problem. I'll type it in green this time.
Tarush is 5 times as old as Arman is today, 85 years ago. We're dealing with huge swathes of time. 85 years ago. Tarush was 10 times as old as Arman. How old is Arman today? Let's see if we can tackle this quite interesting problem, I think. Settings. Pen tool on. OK. Well, I think this might be useful to do one of those charts like we did in the first video presentation. Well, we're trying to solve for how old is Arman today's. So let's say Arman. And we're going to have today. And we're going to have, what's the other time period we're dealing with. We're dealing with 85 years ago. So, let's say. 85 years ago. In a galaxy far, far away. OK, Arman and Tarush. Well, we're trying to solve for how old is Arman today's. So let's just make that x, for simplicity. It says Tarush is 5 times as old as Arman today. So let me underline that. Tarush is 5 times as old as Arman today. So if Arman is x, that tells us that Tarush is going to be 5x. 85 years ago. So, 85 years ago, well, Arman is x today, then 85 years ago, Arman would have been x minus 85. And if Tarush is 5x today, then Tarush would be 5x minus 85. I just subtracted 85 from the current age. Because we're going 85 years in the past.
And now we have this extra piece of information. Which tells us that 85 years ago, Tarush was 10 times as old as Arman. So this number is going to be 10 times more than this number. That's what that sentence tells us. 85 years ago, we're in this situation. Tarush, which is this, was 10 times older than Arman. We just write that out algebraically. 85 years ago, Tarush is 5x minus 85. And the sentence tells us that he was 10 times older than Arman, who is x minus 85. Now we just solve the equation. We get 5x minus 85 is equal to 10x minus 850. And then you get—and I'm going to do this, skip some steps, just to confuse you—5x is equal too—well, I think I just confused myself. 5x is equal to 850 minus 85. Let's see, what's 850 minus 85. It'll be 35 less than 800. So we could say that 5x—35 less than 800. 30 less than 800 gets 770. So 765. And then x is equal to, let me see. 5 goes into 70. 1 times 5. 26. 5 times 5 is 25. 15. So x is equal to 153. We have some long-lifespanned people. So we get the solution that Arman is 153 years old. Today. Let's see if that makes sense. Well, if he's 153, then, no, that can't be right. Because then he's 5. Huh. Well, actually I'm almost out of time. Let me see where I might have messed up on this. If Arman is x, Tarush is 5x. That makes sense. Oh, right, right, right. I think this could make sense. So, I thought that Tarush had to be younger than Arman. But no, Tarush is 5 times 153. So Tarush is actually 765 years old. We should call him Methuselah. So, Tarush is 765 years old. And then if we go 85 years into the past, Tarush would have been—what did we say? If we go 85 years into the past, so let's write this down. This is equal to, I'm about to run out of time, so you might have to check this yourself. If that's equal to 153, then 5x is equal to 765. These numbers are big. And then 153 minus 85. Well, 155 minus 85 would be 73. So this would be 72. And then Tarush, 85 years ago. No, I think I messed up someplace. Well, actually, I only have ten seconds before YouTube won't let me upload it. So we'll have to stop there. Thank you.