
By: drstevewu (offline) Tuesday, January 08 2013 @ 09:34 PM CST (Read 1117 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...

Junior
Registered: 04/20/10 Posts: 27





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.

Active Member
Registered: 04/21/11 Posts: 623





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



drstevewu 
Thank you very much Edward.

Junior
Registered: 04/20/10 Posts: 27



