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By: drstevewu (offline)  Tuesday, January 08 2013 @ 09:34 PM CST (Read 1125 times)  
drstevewu

Is there a better way to solve the following question rather then using "guest and check" method?

Question: There are 140 apples and 200 oranges in Stall X. There are 160 apples and 40 oranges in Stall Y. How many apples and oranges must be moved from Stall Y to Stall X so that 50% of the fruits in Stall X and 75% in Stall Y are apples?

Thank you...Smile

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By: echeewh (offline)  Wednesday, January 09 2013 @ 07:01 AM CST  
echeewh

Hi there,

Following pls find my worked solution:

<Before>
Stall X:
Apples (A): 140 Oranges (O): 200

Stall Y:
Apples (A): 160 Oranges (O): 40

<Process>
Apples and Oranges transferred from Y to X.

<After>
Stall X:
Apples (A): 50% Oranges (O): 50%

A : O
1 : 1


Stall Y:
Apples (A): 75% Oranges (O): 25%

A : O
3 : 1

Apply <Unchanged Total> concept, total number of apples in X and Y (before) = total number of apples in X and Y (after). The same goes for oranges.

Using parts (p) and units (u) method (Simultaneous method), let number of fruits in X (after) be parts (p) and number of fruits in Y (after) be units (u).

1p + 3u --> 140 + 160 = 300 -- (1) {apples in X and Y}
1p + 1u --> 200 + 40 = 240 -- (2) {oranges in X and Y}

(1)-(2):
3u - 1u --> 300 - 240
2u --> 60
1u --> 30

So, number of A left in Y: 3u --> 3 × 30 = 90
number of O left in Y: 1u --> 30

Hence, number of A transferred: 160 - 90 = 70
number of O transferred: 40 - 30 = 10

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

Trust this helps.

Do let me know again if this is different from your AnswerKey or if there's any clarification.

Cheers,
Edward.

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By: drstevewu (offline)  Sunday, January 13 2013 @ 07:40 AM CST  
drstevewu

Thank you very much Edward.Smile

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