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My 7 year old son was given this question as a sort of bonus question and although I managed to solve it using some really awful simultaneous equations I can't help but think there is a simpler more intuitive way to solve it. Afterall, it was given to a 7 year old.

The question is this:

Amir, Brett and Carly share some money.
Amir gets a third of the money.
Carly gets 5 times the as much as Brett.
Carly gets £84 more than Amir
How much money does Brett get?

Is there a really simple way to solve this? Any help is much appreciated

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    $\begingroup$ Carly and Brett get $2/3$ of the money, and Carly gets $5/6$ of those two thirds. Compare that to Amir's $1/3$. $\endgroup$
    – dxiv
    Commented Mar 13, 2022 at 19:59
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    $\begingroup$ And they forgot Sam and Freddy, who always share with Carly. $\endgroup$ Commented Mar 13, 2022 at 20:00
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    $\begingroup$ The equations are not awful. $M=3A$ is the money. Then $C=5B=A+84$. Find $B$ in terms of $M$. $\endgroup$ Commented Mar 13, 2022 at 20:03
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    $\begingroup$ @DietrichBurde Probably anything with symbols is awful for a parent who hasn't done maths in years :) $\endgroup$
    – Gareth Ma
    Commented Mar 13, 2022 at 20:06

2 Answers 2

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An attempt to solve it with simple words ...

Brett gets $1$ part.

Carly gets $5$ parts

Carly and Brett get $6$ parts.

As Amir gets one third of the total, it is not difficult to derive that Amir gets $3$ parts.

Carly gets $2$ parts more than Amir: therefore a part corresponds to $42$ pounds.

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  • $\begingroup$ I don't follow your last sentence. Where did the $42$ come from? $\endgroup$ Commented Mar 13, 2022 at 20:20
  • $\begingroup$ @DietrichBurde $42 = 84/2$. These two parts correspond to 84 pounds. $\endgroup$
    – Damien
    Commented Mar 13, 2022 at 20:22
  • $\begingroup$ I see. For me, the equations are indeed easier. No clever argument required :) $\endgroup$ Commented Mar 13, 2022 at 20:23
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    $\begingroup$ Yes!!!! Going back to age 7… I don’t understand but I would at eight. $\endgroup$
    – gnasher729
    Commented Mar 13, 2022 at 20:24
  • $\begingroup$ @DietrichBurde This answer (+1) looks to me like the intended solution in the given context. Here is my paraphrase: suppose Brett got $1$ pound, then Carly got $5$, and Amir got half of Brett's and Carly's total, so $3$ pounds, which means $(A,B,C) = (3, 1, 5)$. Then Carly got $5-3=2$ pounds more than Amir, but we know that in reality the difference was $84$ pounds, which is $42$ times higher. Since the problem is linear, the solution must be $\,42 \times (3, 1, 5)\,$. Of course, a $7$-year old won't argue that "the problem is linear", but they might still have an intuition for how it works. $\endgroup$
    – dxiv
    Commented Mar 14, 2022 at 2:37
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A gets 1/3rd. C gets 1/3rd + 84. B gets 1/15th + 16.8. Total = 11/15th + 100.8. So 4/15th of the total is 100.8, 4 times total = 1512, total = 378. Let’s check:

A gets 128, C gets 212, B gets 43 - that’s why you check :-)

No, A gets 126, C gets 210, B gets 42, total 378 :-) A bit hard for 7 year old. I’d have done it at 10, but not at 7.

You could have solved with binary search for the total. 1200 is too much, 600 so too much, 300 is too little, 450 is too much etc. That is possible for a determined 7 year old IMO.

Or try total = 100, 200, 300, 400. Calculate what each one gets, and if total <= 300 you find that total is less than total. With total = 400 you find that total > total. Then you try the values in between. Can a seven year old use a spreadsheet?

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    $\begingroup$ OPs seven year old son was given the question. $\endgroup$
    – gnasher729
    Commented Mar 13, 2022 at 20:18
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    $\begingroup$ "For a friend" also was always given in the posts, I know. By the way, you should use MathJax. Here is a tutorial. $\endgroup$ Commented Mar 13, 2022 at 20:18
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    $\begingroup$ Richsell, Damien’s answer is excellent. $\endgroup$
    – gnasher729
    Commented Mar 13, 2022 at 20:27
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    $\begingroup$ BTW, can your son use a spreadsheet? It’s a very, very useful maths tool. $\endgroup$
    – gnasher729
    Commented Mar 13, 2022 at 20:31

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