Before & after Maths Questions

zman09 on 07/07/2022 - 17:38
Last edited 07/07/2022 - 17:39

Following on from https://www.ozbargain.com.au/node/704951 I have been trying and failing to understand how before and after maths questions can be answered by using units. I have been watching some YouTube videos but for the life of me I still cannot grasp how the units are split. I get some questions like asking about changes in ratio and what they had at the beginning when they give all the details but for question like the following I get stumped.

Bob had 3 times as much money as Dave. After each of them spent $180, Bob had 5 times as much money as Dave. How much did each of them have at first?

Apparently the approach is to make 1 unit as 360? But how do they get to this figure in the first place?

This is a year 5 maths question doh

Education & Work

Comments

  • whatwasherproblem on 07/07/2022 - 17:43

    360 is the solution, right? i.e. the amount of money Dave has?

    Not sure how you'd get to that figure using units(?) but solving the equations simultaneously is easy enough.

    • zman09 on 07/07/2022 - 17:56

      360 is part of the solution (one unit) but I don’t get it.

      • whatwasherproblem on 07/07/2022 - 17:58

        Got a link to one of the Youtube vids handy? I'm as confused as you are about what this method of 'units' is. I would've just done the math problem the way pinchies did it below.

          • whatwasherproblem on 07/07/2022 - 18:34
            +1

            @zman09: I sort of get it, I suppose? It seems like a really visual method where you'd draw the Before situation (i.e. Bob has 3x as much money as Dave, so Bob's box is 3 times longer), then visually subtract off 180, and then visually compare the remainders so that you get the After situation (where Bob has 5x as much money as Dave). From there you pick out a common 'unit' of measurement and solve the thing geometrically.

            e.g. If I were to draw it out crappily in text:

            Step 1) Before (Bob has 3x as much money as Dave):
            B: [=====|=====|=====]
            D: [=====]

            Step 2) Subtract 180 (doesn't need to be exact, but assume it's 'somewhere in the middle of the amount of money Dave has'):
            B: [=====|=====|==……]
            D: [==…..]

            Step 3) After (Bob has 5x as much money as Dave):
            B: [==||==||==||==||==]
            D: [==]

            And then comparing Steps 2 and 3 you 'figure' that for those amounts to be equal, i.e.
            B (step 2): [=====|=====|==……]
            B (step 3): [==||==||==||==||==]
            then that smaller unit [==] has to be exactly half of the bigger unit [==……] and matches the quantity that was subtracted (the $180). So the bigger unit is twice that, or $360.

            I dunno, seems a bit silly to me. It reminds me of the 'lines' trick for multiplying numbers: a cool geometric 'party trick' to show to little kiddies, but quickly replaced with quicker and more robust methods that don't require drawing things.

            • zman09 on 07/07/2022 - 18:53
              +1

              @whatwasherproblem: Wow ty for putting in the effort to write that up. That does make sense and I agree seems to be a lot of effort when other methods are quicker and more efficient.

  • pinchies on 07/07/2022 - 17:44
    +34

    (1): Bob = 3x Dave
    (2): Bob - 180 = 5x (Dave -180)

    Sub in 1 into 2
    3x Dave -180 = 5x (Dave - 180)

    3x Dave - 180 = 5xDave - 5x180
    4x180 = 2xDave
    Dave = 360

    Sub into (1)
    Bob =1080

  • Eatslikeacat on 07/07/2022 - 17:47
    +4

    The solution is Pepsi! I get partial credit.

  • RichardL on 07/07/2022 - 18:11
    +1

    At the start

    B:D
    3:1 (Difference of 2)

    After spending $180 each

    B:D
    5:1 (Difference of 4)

    As they both spent the same amount of money, the difference should still be the same, therefore you times the original ratio by 2 (to match the difference)

    B:D (Start) -> B:D (End)
    6:2 -> 5:1

    As they both lost 1 ratio and both spent the same amount, 1 ratio = $180

    Bob = 6 x $180 = $1080
    Dave = 2 x $180 = $360

    It been a while since I've done primary maths, so I could be wrong

    • zman09 on 07/07/2022 - 18:18

      This makes a lot of sense but the thing I still cannot grasp is why would the 1x ratio be $180?

      • RichardL on 07/07/2022 - 18:21
        +1

        Both Bob and Dave Ratio dropped 6->5 and 2->1 respectively and they both spent the same $180; therefore you can conclude that 1 ratio = $180.

        • zman09 on 07/07/2022 - 18:33

          Will need to read through this a few times to get it but starting to make sense now! Ty

  • [Deactivated] on 07/07/2022 - 18:29
    +4

    It's been so long since you were in school that it doesn't make sense to you. Also, this kind of thing probably wasn't even taught back then, and certainly not in the same way.

    The problem is, you needed to be aware of what was being taught up to that point, and then this would be trivial. Your confusion is also what happens when children fail to grasp the earlier teachings. If they start to fall behind, they end up just as confused as you are.

    • zman09 on 07/07/2022 - 18:32

      You could be right, year 5 for me was 25 years ago, I don’t remember doing anything like this, do remember playing digger from a floppy disc though :)

  • GordonR on 07/07/2022 - 19:26
    +2

    Read pinchies answer, because that is the right way to do it.

    In general:

    Give names to the quantities you need, i.e. Bob and Dave or (B and D)

    There are two unknown values, so you will need to find two equations relating them in the text of the question.

    The first one is “Bob has three times as much money as Dave”
    The second one is “After spending 180, Bob has five times as much money as Dave”

    Then use one equation to get B in terms of D, and substitute into the second equation, which now involves only D to find D.

    Always, always - give names to the unknown values, find equations from the question, because this will work in any context.

    (Disclaimer: yes, this only works as stated for linear equations.)

  • avoidfullprice on 07/07/2022 - 19:58
    +1

    At year 5 level, I don’t think kids are expected to solve this using pro-numerals but rather trial-and-error. (I just check their curriculum)

    Kids would guess the smaller number (Dave) using multiple of the $180, to get whole number answers. They would know Dave has more than $180 in the beginning, because otherwise Dave will have $0 in the end, so Bob can’t have more than $0 but at the same time 5x$0….

    So their next guess would be $360, $540 …

    Not sure how the 1 unit = $360 come about in your provided solution

  • Benoffie on 07/07/2022 - 21:12
    +1

    This is why I became a History teacher 🤣

    • SF3 on 07/07/2022 - 21:57
      +1

      pinchies's comment was posted 4hours ago, so that can be taught :)

  • blitz on 07/07/2022 - 23:41
    +2

    Simultaneous equations is the right way to do this. @pinchies has the right answer.

  • skid on 08/07/2022 - 09:44

    Kids are smart these days, because simultaneous equations were around Year 8 level back in my day.

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