Monday, October 25, 2010

MGS 2010 P6 Prelim P2 Q11:

Ellen and Lenny have some sweets. If Ellen gives away 12 sweets, the number of sweets Ellen has is 13/24 of the total number of sweets that both of them have. If Lenny gives away 12 sweets, the number of sweets Lenny has is 3/8 of the total number of sweets that both of them have. How many sweets do they have altogether? [4 marks][Answer given: 156 sweets]


24  -  13  =  11

E  --  13 u  +  12

L  --  11 u


8  -  3  =  5

L  --  3 p  +  12

E  --  5 p


11 u  -->  3 p  +  12

13  u  +  12  -->  5 p


15 p  -->  55 u  -  12 x 5  =  55 u  -  60

15 p  -->  39 u  +  12 x 3 =  39 u  +  36


55 u - 60  -->  39 u  +  36


16 u  -->  36  +  60  =  96

1 u  -->  96 / 16 = 6

24 u  -->  24  x  6  =  144

144  + 12  =  156  sweets

They have  156  sweets altogether.

2 comments:

  1. can you solve this by using bar models instead of algebra?

    also can you review this approach that gives another answer:

    UsingGap & Difference using Unchanged Total

    Case 1: E gives away 12 sweets
    E : L
    13 : 11 (24units)

    Case 2: L gives away 12 sweets
    E : L
    5 : 3 (8units)
    15 : 9 (24units)

    2units --> 12
    1unit --> 6

    Totla --> 24units --> 24 x 6 = 144

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  2. The "UsingGap & Difference using Unchanged" doesn't seem right. It assumes that Ellen and Lenny have same number of sweets initially, that lead the person to think that 12 sweets give away is the difference of ratio (2 units).

    ReplyDelete