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By: achieve_goal (offline)  Sunday, July 22 2012 @ 04:27 AM CDT (Read 824 times)  
achieve_goal

1. A tailor had some buttons. She used 2/3 of the buttons for some shirts and 1/4 of the remainder for

some dresses. She bought another 1008 buttons and had twice the number of buttons and had twice the

number of buttons she had at first. How many buttons had she at first?

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By: echeewh (offline)  Monday, July 23 2012 @ 08:28 AM CDT  
echeewh

Hi there,

Following pls find my worked solution:

Notes:
Combined Model not drawn to scale.
*** - buffer space for alignment purpose

At first, number of buttons is split into 3 parts, of which 2 parts were used for shirts (S). From remaining 1 part, (1/4) of it was used for dresses (D), thereby, further dividing this into smaller 4 units (4u). Likewise, the other 2 parts used for S are further divided into 8u (1 part = 4u) as shown in model.

<-----------------S------------->
|-----------------|-----------------|-----|----|----|----|------------------------------------------------------------------------------------------|
****************************<D>
<--------------8u--------------><-------4u------->-----------------------------------------1008----------------------------------------->
*********************************<---------------------------------------------------2p------------------------------------------------>
<-------------------1p------------------------------>

After buying another 1008 buttons (3u + 1008), the number of buttons was twice that at first (shown in above model as 2p). The original number of buttons (12u) is the 1p. Now we have ...

3u + 1008 --> 2 x 12u
3u + 1008 --> 24u
21u --> 1008
1u --> 48

Number of buttons at first = 12u --> 12 x 48 = 576

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

Trust this helps.

Do let me know again if this is different from your Answerkey or if you have further clarifications.

Cheers,
Edward

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