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 Gap & Difference Concept
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By: JessicaTan (offline)  Thursday, August 16 2012 @ 03:53 AM CDT (Read 2492 times)  
JessicaTan

Hi, kindly help me please.

3) Alice, Betty and Christina have some cookies each. If Alice gives 4 cookies to Betty, both of them will have an equal number of cookies. If Betty gives 4 cookies to Alice, Alice will have thrice as many cookies as Betty. Christina's share is the sum of the other two girls share. How many cookies do the three girls have altogether?



4) Martin and Leo have some marbles each. If Martin gives Leo 24 marbles, they will have an equal number of marbles. If Martin gives Leo 56 marbles, Martin will have 1/3 as many marbles as Leo. How many marbles does Martin have at first?


5) If Ismail buys 3 packets of biscuits and 4 packets of seaweed, he will have $4.50 left, if he buys 3 packets of seaweed and 4 packets of biscuits, he will have $3.50 left. Given that a packet of seaweed costs $6, find the amount of money he have at first.


rdgs

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By: echeewh (offline)  Saturday, August 18 2012 @ 07:30 PM CDT  
echeewh

Hey Jessica,

Typically for questions of this nature, the 1st IF will help you establish/determine the starting/before model as shown below:

Q3.

<1st IF>
<after>

A: |---------------|
B: |---------------|

<before>

A: |------------------|<-4->|
B: |----------|<-4->

<2nd IF>
<after>

** <------------ 3u ---------------->
A: |-----------|<---- 8 --->|<-4->|
B: |-----|<4>
** <1u>

C: A + B

Comparing A,B <after> models, we have ...

Gap = 4 + 8 + 4 = 16
Diff = 3u - 1u = 2u

2u --> 16
1u --> 8

<before>

A = 3u - 4 --> (3 x 8) - 4 = 24 - 4 = 20
B = 1u + 4 --> 8 + 4 = 12
C = A + B = 20 + 12 = 32

Total (A+B+C) = 20 + 12 + 32 = 64

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

Q4

<1st IF>
<after>

M: |------------------|
L: |------------------|

<before>

M: |------------------|<--24-->|
L: |-------|<--24-->

<2nd IF>
<after>

** <1u>
M: |--|<8>
L: |-------|<----------56----------->|
** <---------------3u---------------->


Gap = 8 + 56 = 64
Diff = 3u - 1u = 2u

2u --> 64
1u --> 32

M (at first) = 1u + 8 + 48 --> 32 + 56 = 88

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

Q5

<-- 3B + 4S---->
|---------------------|<--450-->|

<--- 4B + 3S----->
|-----------------------|<-350->|

Comparing above 2 models, we have ...

Gap = 450 - 350 = 100
Diff = (4B + 3S) - (3B + 4S) = B - S

B - S = 100

Given that S = 600, we have ...

B - 600 = 100
B = 100 + 600 = 700

Amount (at first) = (3B + 4S) + 450
= [(3 x 700) + (4 x 600) + 450]
= 2100 + 2400 + 450
= $49.50

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

Trust these help.

Do let me know again if these do not agree with your Answerkeys or if there's any clarification.


Cheers,
Edward

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Posts: 625

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