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 By: JessicaTan (offline)  Saturday, January 12 2013 @ 10:24 PM CST (Read 983 times)
JessicaTan

Hi, anyone can help with working solution.

D had 80 more stickers than K. D gave 25% of his stickers to K. K in return gave 60% of her stickers to D. In the end, D had 92 stickers more than K. How many stickers did D have at first?

(ans : 108)

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Registered: 10/17/09
Posts: 82

 By: echeewh (offline)  Sunday, January 13 2013 @ 12:36 AM CST
echeewh

hi Jessica,

Following pls find my worked solution:

D had 80 more stickers. Since D gave 25% (1/4) to K, we can divide the equal portion of both D and K into 4 units (u) each as shown below:

<before>

D |--|--|--|--|<- 80 ->| --> 4u + 80
K |--|--|--|--| ******* --> 4u

<process>

D gave 25% (1/4) to K.
(1/4) × (4u + 80) = 1u + 20

so ...
D = 4u + 80 - 1u - 20 = 3u + 60
K = 4u + (1u + 20) = 5u + 20

In return, K gave 60% (3/5) to D.
(3/5) × (5u + 20) = 3u + 12

so, ... { the <after> model }
D = 3u + 60 + 3u + 12 = 6u + 72
K = 5u + 20 - 3u - 12 = 2u + 8

Given D had 92 stickers more than K at the end,

D - K = 92
6u + 72 - 2u - 8 --> 92
4u --> 92 - 72 + 8 = 28
1u --> 7

D (at first) = 4u + 80
--> (4 × 7) + 80 = 108

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

Trust this helps.

Do let me know again if theres further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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