
By: jennefer_06 (offline) Wednesday, April 11 2012 @ 11:13 AM CDT (Read 1800 times)



jennefer_06 
Help needed for this question.
Grandma had some yellow and purple sweets in the ratio of 9:7. On monday, she made 54 more yellow sweets. On Tuesday, she gave away 44 purple sweets and sold 129 yellow sweets. The number of yellow sweets to the number of purple sweets became in the ratio of 6:5. How many yellow sweets are there in the end?

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By: MathIzzzFun (offline) Thursday, April 12 2012 @ 01:45 AM CDT



MathIzzzFun 

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Registered: 04/02/10 Posts: 36





By: echeewh (offline) Thursday, April 12 2012 @ 05:52 AM CDT



echeewh 
Hey Jennefer,
In addition to MathizzzFun's solution using CrossMultiply method ( a very similar method to that used in OnSponge  Conquer Problem Sums ), one other method is the Simultaneous method ( aka Compare & Replace / Elimination method ).
This is it ....
Number of Yellow (Y) sweets sold by Tuesday = 129  54 = 75
Y : P
9 : 7
75  44
6 : 5
Since the before and after unit qty are different, we denote this by unit (u) and part (p) for before and after respectively as follows:.
9u  75 = 6p
7u  44 = 5p
Rewriting the above, we have:
9u  6p = 75  (1)
7u  5p = 44  (2)
As the question is interested in finding the yellow sweets at the end (which is the part (p) qty ), we shall eliminate the unit (u) qty as follows:
(1) x 7: 63u  42p = 525  (3)
(2) x 9: 63u  45p = 396  (4)
(3)  (4): 42p + 45p = 525  396
3p > 129
1p > 43
Number of Yellow sweets at the end = 6p > 6 x 43 = 258
==================================================
Trust the above technique helps.
Cheers,
Edward

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