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By: JessicaTan (offline)  Tuesday, January 15 2013 @ 06:34 AM CST (Read 1978 times)  
JessicaTan

Hi, please help with working solution. (I do not have answer key)


Eric had some blue marbles and red marbles in the ratio of 1:3. He exchanged some red marbles for the same number of blue marbles. The ratio of the number of blue marbles to the number of red marbles became 4 : 3. How many blue marbles and red marbles did Eric have at first?


Cry


Rdgs
jessica

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By: echeewh (offline)  Tuesday, January 15 2013 @ 06:07 PM CST  
echeewh

Hi Jessica,

Following pls find my worked solution:

** - alignment purpose

Since this is an internal transfer / exchange process (red marbles exchanged for same number of blue marbles), this means total number of Red (R) + Blue (B ) marbles before and after will remain same / unchanged.

<before>

B : R * Total
1 : 3 **** 4

<process>

1 : 1 {exchanged R for B}

<after>

B : R * Total
4 : 3 **** 7

Applying <Unchanged Total> concept here, multiply <before> ratio 7x, <after> ratio 4x.

<before>

B : R * Total
7 : 21 ** 28

<after>

B : R * Total
16 : 12 * 28

Now, we have 9u of R taken out in exchange for 9u of B added back, and its a 1:1 exchange.

hence, Eric had 7 blue and 21 red marbles at first.

===============

Trust this helps.

Do let me know again if theres further clarification.

Cheers,
Edward

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By: JessicaTan (offline)  Wednesday, January 16 2013 @ 04:04 AM CST  
JessicaTan

Thanks Edward for your explanation



Smile Jessica

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By: wendy216 (offline)  Wednesday, February 13 2013 @ 06:36 PM CST  
wendy216

The Question is not correct, you can't get what Eric had at first!

you only know the ratio of blue and red marbles that Eric had at first is 7:21.
for example: eric had 14 blue, and 42 red and he use 18 red change to 18 blue,
left 32 blue, and 24 red ... also satisfy the 4:3 condition

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By: rashida (offline)  Monday, February 18 2013 @ 06:56 AM CST  
rashida

No Edwards right
Cool

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By: Terribleplayer (offline)  Tuesday, February 19 2013 @ 01:29 PM CST  
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Quote by: rashida

No Edwards right
Cool



No, Wendy is correct. With the info given, we can find that 9 units of red were exchanged for an exact same number of 9 units of blue. However, we do not know what exact value 1 unit is! Perhaps some info was left out in the question?

The internal transfer (total unchanged) method is to help us identify how many units are added or subtracted so that we can then tag that number of units to a certain value given. Then the standard route would be to find 1 unit followed by whatever is required by the question. Usually when a value is missing such that we cannot associate the units obtained with a value, the required answer is to state the relationship as a ratio, fraction or percentage (which does not require knowing the exact values).

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By: echeewh (offline)  Wednesday, February 20 2013 @ 11:45 PM CST  
echeewh

Dear Viewers,

Thank you for your views.

In fact all of you are correct (for those who responded). This is subject to individual perspective. The 7 : 21 solution provided by me is the lowest / smallest proportion of blue and red marbles respectively that could fit into the question. Hence any multiple of that could also be a possible answer.

As one of the viewers put it, "Perhaps some info were left out from the question". Maybe yes...maybe no... this will be left for the "setter" to decide.

Regardless of how the question is being set , importantly is to provide a feasible solution to it. The objective is to help students on how to approach the question and apply the concept and skill.

Cheers,
Edward

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