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TOPIC: P5 Nanyang 2009 SA2 Q17: Working Backwards

P5 Nanyang 2009 SA2 Q17: Working Backwards 4 years 3 months ago #1

Hi guy..need help..

Jolens and Penny had a sum of money. Jolene gave Penny 0.4 of her money. Penny then gave Jolene 1/2 of her money. In the end, Jolene had three times the amount of money that penny had. If Jolene gave penny $125 more than what Penny Gave Jolene, How much money did Jolene have at first ? :(
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Re:P5 Math Unchanged Total working backwards 4 years 3 months ago #2

Jolens and Penny had a sum of money. Jolene gave Penny 0.4 of her money. Penny then gave Jolene 1/2 of her money. In the end, Jolene had three times the amount of money that penny had. If Jolene gave penny $125 more than what Penny Gave Jolene, How much money did Jolene have at first ?

For this question they each give to each other, so the totals remain the same throughout. We can just work backwards using ratios to solve it.


J : P
3 : 1 (At end & After Jolene gave 50% to Penny)
2 : 2 (Before Penny gave 50% to Jolene)
3 : 3 (Change to a ratio that has 6/10 left --> 3/5)
5 : 1 (At first, before Jolene gave 40% to Penny)

The question asks us to compare the number of units they gave to each other. So we need to ensure the ratios are comparable throughout. If you notice I originally changed the ratio of 2 : 2 to 3 : 3 in the middle so that we could take 50%.

J : P
9 : 3 (At end & After Jolene gave 50% to Penny)
6 : 6 (After Jolene gave 40% and before Penny gave 50%)
10 : 2 (At first, before Jolene gave 40% to Penny)

Jolene gave to Penny 4units
Penny gave to Jolene 3units
difference is 1unit
1unit --> $125
Jolene at first $1250
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Re:P5 Math Unchanged Total working backwards 4 years 3 months ago #3

Hi Chris, can use model drawing for this problem sum because I don't understand how you can the ratio 2:2, 3:3 etc....

Thanks
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Re:P5 Math Unchanged Total working backwards 4 years 3 months ago #4

Yes, you will be able to use a model. While a model will work, it is going to be tedious especially since this question has only two transfers. Other questions of this type might involve 3 or 4 transfers making it very difficult and prone to make mistakes.

If you are in P5, you should understand using Ratios as I have shown. If you are not in P5 yet - don't worry about this question :)

If your problem is just changing of 2:2 to 3:3, then you could choose any number to show they are the same. 1:1, 2:2, 10:10, u:u. This is similar to the equivalent fractions. 1/2 = 2/4 = 3/6, etc.

Why don't you try drawing out the model and using the ratios as a comparison to see how you do?
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Re:P5 Math Unchanged Total working backwards 4 years 2 weeks ago #5

Hi Chris, can you help with the steps to put the answer back to check that it is correct? I am a bit lost and am unable to help my son.

Thank you.
Cheers, Janet
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Re:P5 Math Unchanged Total working backwards 4 years 2 weeks ago #6

Hi Janet,

Here is a more detailed solution. I tried to encapsulate my thoughts my showing the workings on the right - matching the problem sum. Also notice the reasons / explanations on the left.

I do recommend that he learns such questions as they are becoming more and more common. If you look at this years SA1 and Prelims you will see a bunch. The primary difference is that this question is only 2 steps where others have 3.

Attachments:
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Nanyang Primary 2009 P5 SA2 Paper 2 Q17 4 years 2 weeks ago #7

Hi Chris,

For reference purpose, could you pls edit the title of this post to include the source of this question -> Nanyang Primary 2009 P5 SA2 paper 2 Q17 - 5 marks posted by Andrew Lee?
Thanks.
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Re: Nanyang Primary 2009 P5 SA2 Paper 2 Q17 4 years 2 weeks ago #8

Exactly what I try to do, if it's given of course :)
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Re:P5 Math Unchanged Total working backwards 4 years 1 week ago #9

Hi Chris, thank you for your detailed explanation. Actually I was hoping you can help to put the answer (ie Jolene had $1250) back into the equation, find out how much should Penny has at first too and confirmed that 1250 is the correct answer. Do you think it makes sense?

Thank you very much for your help
Cheers, Janet
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Re:P5 Math Unchanged Total working backwards 4 years 1 week ago #10

Yes that makes perfect sense. I would encourage "and train" your child to perform this check when doing the work. In this case we have the value of 1unit so you can take 10units and 2units and then work through the question from start to finish to compare the end result. Why don't you try it and see what you get? It works for me :)
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