Old school equations with Sal
Age word problems 2 Second set of age word problems
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- 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 one hundred and eight 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 one hundred and eight years old.
- Jonathan is twenty-four years old.
- How many years will it take for Salman to be exactly four
- 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 four times Jonathan's age.
- Well, if today, I, or Sal, if Salman, it's hard to speak
- in the third person.
- If Salman is one hundred years old today, in y years, Salman
- will be one hundred and eight plus y is equal to Sal in y years.
- We'll say y years.
- Sal in y years is going to be one hundred and eight plus y.
- And then Jonathan in y years, that's pretty easy.
- He's going to be twenty-four 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 four times as old as Jonathan?
- Well, and the exactly is important.
- Because Salman is already more than four times
- as old as Jonathan.
- But they want to figure out exactly when is Salman going to
- be four times as old as Jonathan.
- Well, in y years Salman is going to be one hundred and eight plus y.
- So we know that.
- one hundred and eight plus y.
- And after y years, he's going to be four times
- as old as Jonathan.
- Exactly four times.
- And Jonathan's going to be twenty-four plus y years old.
- And now we just solve the equation.
- Get one hundred and eight plus y is equal to four times twenty-four.
- Well, four times twenty-five is one hundred.
- And we can subtract four from there.
- So it's ninety-six.
- Plus foury.
- And now we just solve this equation.
- We get three.
- three, I'm going to skip some steps, because I think this
- part is easy for you.
- threey will equal one hundred and eight minus ninety-six.
- So we get threey is equal to, what is that, twelve, right?
- So y is equal to four.
- So our algebra has told us that in four years Salman is going
- to be exactly four times as old as Jonathan.
- Let's see if that's true.
- Well, if Salman is one hundred and eight right now, in four years
- he's going to be one hundred and twelve.
- And if Jonathan is twenty-four right now, in four years he's
- going to be twenty-eight.
- And let's see.
- twenty-eight times four is eighty plus thirty-two.
- Yep, exactly.
- He'll be one hundred and twelve.
- 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 five times as old as Arman is today, eighty-five years ago.
- We're dealing with huge swathes of time.
- eighty-five years ago.
- Tarush was ten 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 eighty-five years ago.
- So, let's say.
- eighty-five 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 five times as old as Arman today.
- So let me underline that.
- Tarush is five times as old as Arman today.
- So if Arman is x, that tells us that Tarush is going to be fivex.
- eighty-five years ago.
- So, eighty-five years ago, well, Arman is x today, then eighty-five years ago,
- Arman would have been x minus eighty-five.
- And if Tarush is fivex today, then Tarush would be fivex minus eighty-five.
- I just subtracted eighty-five from the current age.
- Because we're going eighty-five years in the past.
- And now we have this extra piece of information.
- Which tells us that eighty-five years ago, Tarush was ten
- times as old as Arman.
- So this number is going to be ten times more than this number.
- That's what that sentence tells us.
- eighty-five years ago, we're in this situation.
- Tarush, which is this, was ten times older than Arman.
- We just write that out algebraically.
- eighty-five years ago, Tarush is fivex minus eighty-five.
- And the sentence tells us that he was ten times older than
- Arman, who is x minus eighty-five.
- Now we just solve the equation.
- We get fivex minus eighty-five is equal to tenx minus eight hundred and fifty.
- And then you get-- and I'm going to do this, skip some
- steps, just to confuse you-- fivex is equal too-- well, I think
- I just confused myself.
- fivex is equal to eight hundred and fifty minus eighty-five.
- Let's see, what's eight hundred and fifty minus eighty-five.
- It'll be thirty-five less than eight hundred.
- So we could say that fivex-- thirty-five less than eight hundred.
- thirty less than eight hundred gets seven hundred and seventy.
- So seven hundred and sixty-five.
- And then x is equal to, let me see.
- five goes into seventy.
- one times five.
- twenty-six.
- five times five is twenty-five.
- fifteen.
- So x is equal to one hundred and fifty-three.
- We have some long-lifespanned people.
- So we get the solution that Arman is one hundred and fifty-three years old.
- Today.
- Let's see if that makes sense.
- Well, if he's one hundred and fifty-three, then, no, that can't be right.
- Because then he's five.
- 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 fivex.
- 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 five times one hundred and fifty-three.
- So Tarush is actually seven hundred and sixty-five years old.
- We should call him Methuselah.
- So, Tarush is seven hundred and sixty-five years old.
- And then if we go eighty-five years into the past, Tarush would have
- been-- what did we say?
- If we go eighty-five 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 one hundred and fifty-three, then fivex is equal to seven hundred and sixty-five.
- These numbers are big.
- And then one hundred and fifty-three minus eighty-five.
- Well, one hundred and fifty-five minus eighty-five would be seventy-three.
- So this would be seventy-two.
- And then Tarush, eighty-five 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.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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