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Age word problem: Imran

Sal solves the following age word problem: In 40 years, Imran will be 11 times as old as he is right now. How old is he right now? Created by Sal Khan.

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  • female robot grace style avatar for user kittychan
    please someone help me....I am homeschooled and i don't know how to solve these questions....so please can someone tell me how to solve these questions..I will be really grantfull to you even if you just helped me out in only one question!!..thanks

    1.Mary's age is 2/3 that of Peter's.Two years ago Mary's age was 1/2 of what Peter's age will be in 5 years' time.How old is Peter now?

    2.A half of what John's age was 4 years ago is equal to one third of what it will be in 5 years' time.How old is John now?>>>thanks<<<
    (16 votes)
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    • blobby green style avatar for user DeWain Molter
      Define m as Mary's age, p as Peter's age, convert the problem into algebra notation.

      1.Mary's age (m) is(=) 2/3 that of Peter's((2/3)*p).Two years ago Mary's age(m-2) was(=) 1/2 of what Peter's age will be in 5 years' time[(1/2)*(p+5)].How old is Peter now?

      Get two equations...
      m=(2/3)*p, and
      (m-2)=(1/2)*(p+5), multiply 2nd eqn by 2 to eliminate fraction, so system is

      m = (2/3) p
      2m - 4 = p + 5, substitute value of m from 1st eqn into 2nd eqn, get

      2((2/3)p) - 4 = p + 5, solve for p... simplify multiplication first

      (4/3)p - 4 = p + 5, add 4 to both sides, get

      (4/3)p = p + 9, subtract p from both sides, get
      (1/3)p = 9, multiply both sides by 3 to eliminate fraction, get
      p=27, Peter is 27 years old.

      2.A half of what John's age was 4 years ago[(1/2)(j-4)] is(=) equal to one third of what it will be in 5 years' time[(1/3)(j+5)].How old is John now?

      (1/2)(j-4) = (1/3)(j+5), I would multiply both sides by 6 to eliminate all the fractions... get
      3(j-4) = 2(j+5), work through distributive property
      3j - 12 = 2j + 10, add 12 to both sides
      3j = 2j + 22, subtract 2j from both sides
      j = 22
      (33 votes)
  • leaf grey style avatar for user The Painter
    I am having a lot of trouble solving these types of problems on the "Age word problem" questions. Could someone help me with this?
    Here's an example:
    Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
    How old is Daniel now?
    (11 votes)
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    • aqualine ultimate style avatar for user Timber Lin
      let k=kevins age now
      let d=daniels age now
      k=d+3, kevin is 3 yrs older than daniel now.
      2 years ago, kevin was k-2 years old, daniel was d-2 years old, and kevin was 4 times daniels age:
      (k-2)=4(d-2), which becomes k-2=4d-8 then k=4d-6. we also know k=d+3 since kevin is 3 years older than daniel now. if you substitute for k, then 4d-6=k=d+3.
      4d-6=d+3, 3d=9, d=3.
      daniel is 3 years old now.
      hope this helps
      (19 votes)
  • piceratops seed style avatar for user Nocato Kasler
    When viewing these videos in the 8th grade, "Systems of equations" playlist, the elimination method of solving a system of equations has not been introduced.

    This is jarring. It would be nice if the elimination method was introduced earlier, or these videos just used the substitution method.
    (11 votes)
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  • blobby green style avatar for user Adith Williams-white
    How do i solve this problem, please help
    The sum of the ages of Jennie and Matt is 40. Jennie is 5 less than twice Matt's age. How old is Matt?
    (8 votes)
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    • male robot hal style avatar for user THEILLUMINATI666 2.0
      First, you would want to read it over and think of a way to convert this into an equation. so let's say Jennie's age is j and matt's age is m. Jennie's age is 5 less than twice matt's age so jenny's age(j)=2m-5. Jenny's and matt's ages add up to 40 so we know that jenny's age is
      2m-5 and matt's age is m so 2m-5+m=40.
      2m+m-5=40 lets get rid of the 5 so add 5 to both sides
      2m+m=45
      3m=45 (because 2m+m = 2m+1m=3m)
      what times 3 is 45? divide both sides to find out
      m=15 Matt is 15 years old. Jenny is 25.
      (5 votes)
  • starky ultimate style avatar for user AR12
    Kevin is 3years older than Daniel. Two years ago, Kevin was 4times as old as Daniel.

    How old is Kevin now?
    (4 votes)
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  • piceratops tree style avatar for user B
    Help pls!

    Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.

    How old is Ishaan?

    How do I do this?
    (1 vote)
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    • purple pi pink style avatar for user Annabelle
      For anybody who is wondering how to do this...
      Step 1: Determine the unknown values. In this case, the unknowns are Ishann's age and Ben's age.
      Step 2: Assign a variable to the unknown values. For this problem, we will assign the variable y to Ben's age and x to Ishaan's age. Therefore, y=Ben's age and x=Ishann's age.
      Step 3: Set up a system of two equations. The first equation is y=4x, because Ben's age (y) is four times Ishann's age (x). The second equation is y=x+6, because Ben's age (y) is 6 more than Ishann's age (x).
      Step 4: Solve the system using substitution. The two equations are y=x+6 and y=4x. Y is equal to x+6, and y is also equal to 4x. Therefore, we can substitution x+6 for y in the equation y=4x (or vice versa), getting x+6=4x. We can solve this equation to get x=2. We can then find y by plugging 2 in for x in either of the original equations. 2+6=y, so y=8. 4(2)=y, so y=8.

      Ishaan is 2 years old and Ben is 8 years old.
      (5 votes)
  • hopper jumping style avatar for user Mark Ivanovich
    Hi everyone, may be I missed smth, but why, for instance, if somebody in 16 will be as 3 times older as he now, his age at this moment is 8 by an equation like this b+16=3b? If I've reached now eight years old, so, my age times 2 is sixteen, not times three. So, in 16 I'll be as 2 times older as I now. Right? Is in this case some mentality difference of understanding of English or problems of my math understanding?
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      Sounds like the problem is asking you to compare your current age with your age 16 years into the future. You have the equation equation: b + 16 = 3b

      b = your current age NOW, in 2018
      In 16 years, your age becomes b+16
      If your current age = 8, then in 16 years, your age = 8+16 = 24
      Does 24 = 3 times your current age? Yes! 3*8 = 24.

      In your analysis, you are only going 8 years into the future, not 16 years. The problem isn't saying your future age is 16, it is saying "your age in 16 years".
      (2 votes)
  • leafers seed style avatar for user Stago
    I saw all of the age word problems. THEY ARE NOT SYSTEMS! They only use one equation. Not helpful!
    (2 votes)
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    • piceratops ultimate style avatar for user Daria
      They are systems! You are probably making the equations wrong. Some, like this one, may only require one equation. In that case, make sure you have a variable to solve for. Some are more complicated and require 2 equations. For example, say David is 5 years younger than Savanna. In 7 years, David will be 3 times younger than Savanna. What is Savanna´s age? In these problems, one equation will NOT help you. Let D be David´s age and S be Savanna´s age. D+5=S, and D+7=3(S+7). That gives you a system of equations. Whenever you have more than one variable, you NEED to have the same number of equations as the number of variables (three different variables means you need three different equations). Otherwise, you cannot solve the system.
      (2 votes)
  • blobby green style avatar for user juliegreene
    i cant figure out this problem
    Ben is 39 years old and Ishaan is 3 years old.
    How many years will it take until Ben is only 4 times as old as Ishaan?
    (1 vote)
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  • orange juice squid orange style avatar for user morganswain81
    what would you do with the 40 and 11?
    (2 votes)
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    • duskpin sapling style avatar for user SZ
      I'm assuming that you are talking about the equation in the video above. The 40 and 11 were in a equation: 11x=x+40. You would basically solve for x.
      11x=x+40
      subtract x from both sides
      10x=40
      solve for x which means to divide by 10 on both sides to get x alone
      x=4
      The answer would be that Imran is 4 years old right now.
      (1 vote)

Video transcript

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.