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 By: JessicaTan (offline)  Sunday, July 29 2012 @ 02:48 AM CDT (Read 841 times)
JessicaTan

Betty, Siti and Mei Ling had \$5000 altogether. Betty spent 2/5 of her money and Siti spent \$500. The ratio of the amount of money Mei Ling spent to the amount of money Betty spent was 3:4. In the end, they had the same amount of money left.

(a) How much money had each of them left?

(b) What was the total sum of money Betty and Mei Ling had at first?

Answer key : (a) \$1080, (b) \$3420

Thanks
Jessica

Regular Member

Registered: 10/17/09
Posts: 82

 By: echeewh (offline)  Sunday, July 29 2012 @ 08:09 PM CDT
echeewh

Hi Jessica,

One is recommended to start drawing model from where the subjects /persons have the same / equal amount of money / item.

As this appears at the end, we can apply the <Work Backwards> technique and using <Model>, we have the following ...

*** - buffer space for alignment purpose

<After>
B |----------------------|
S |----------------------|
M |----------------------|

<Process>
B: -(2/5), S: -500,
M (spending) : B (spending) = 3 : 4

In <work Backwards>, we just reverse the process.
B:
B was left with 3 parts(p) ; by adding 2p, it will be B's original money. Likewise, divide all 3 equal portions into 3p each.
S: + 500
Ratio of M : B (Spending) = 3 : 4:
Divide B's spending of 2p into 4 equal units (u); Add 3u to M (M's spending);
Likewise, the 3p of each B, S, M is divided into 6u each.

So the <Before> model is derived as shown:

*********************<--- 4u --->
**<-------- 3p -------><--- 2p --->
B |---|---|---|---|---|---|---|---|---|---|**--
S |---|---|---|---|---|---|<-500->*******|--> 5000
M |---|---|---|---|---|---|---|---|---|*****--
**<-------- 6u -------><- 3u ->

Hence, we have ...

25u --> 5000 - 500 = 4500
1u --> 4500 รท 25 = 180

(a) Each of them was left with 6u --> 6 x 180 = \$1080

(b) Total (B + M) had at first = 10u + 9u = 19u
*** 19u --> 19 x 180 = \$3420

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

Trust the above helps.

Do let me know again should there be any clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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