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Help seeing a solution !!!

BickerJane 11 January 2019 10:39
Posts1
Joined07/06/18

Sam had £463 more than Charles. Charles then gave £246 to Sam.

How much more money did Sam have than Charles in the end?

£463 +£246 = £709

I see this part of the problem no worries, but then the solution goes onto:

£709 + £246 = £955

I don't get this part, even using the bar model. Why add £246 again?

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lhooper 11 January 2019 11:08 - Last edited by lhooper on 11 January 2019 11:10
Posts7
Joined05/01/07

Sam's' total has increased by £246, and Charles' total has decreased by £246. So the difference (ie the extra money held by Sam) has increased by 2 x £246.

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Laurie_Jacques 11 January 2019 11:22 - Last edited by Laurie_Jacques on 11 January 2019 11:24
Posts535
Joined27/06/06

Hi Jane,

I posted an image of the bar model to represent the two stpes of the calculation.

Algebraically:

S = amount Sam has

C = amount Charles has

S = N + £463

C = N

Difference is: S - C = (N + £463) - N = £463

Charles gives Sam £246

So no

C = N + £463 + £246

S = N - £246 (Sam now has £246 less than before)

Difference is: S - C = (N + £463 + £246) - (N - £246)

= N + £463 + £246 - N + £246

Difference = £463 + £246 + £246

Using countable objects you can see that if C had 6 objects and S had 5 the difference is 1.

If S gives 1 object to C then S has 1 more than before and C has 1 less than before so the difference is actually 3. (The original difference + double the amount given by S)

C xxxxxx

S xxxxx

C xxxxxxx

S xxxx

It an interesting problem to explore.

So what would happen next if C gave S another one object when the difference is 3?

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