
By: Tping (offline) Tuesday, May 01 2012 @ 12:48 AM CDT (Read 1516 times)



Tping 
Hi, pls help to solve following quention, tks.
Q1
There were 864 more chocolate muffins than banana muffins in a shop.
After 1/6 of the chocolate muffins and 3/4 of the banana muffins were sold,
there were 1728 more chocolate muffins than banana muffins left.
How many chocolate muffins were there at first?
Q2
Dinesh had some red pens and blue pens.
1/7 of the pens were red.
After he had sold 1/3 of the red pens
and bought half as many blue pens as before,
he had 87 red and blue pens in the end.
a) What is the ratio of the number of red pens to the number of blue pens in the end?
b) How many blue pens did he have at first?

Junior
Registered: 01/26/12 Posts: 25





By: echeewh (offline) Tuesday, May 01 2012 @ 04:59 AM CDT



echeewh 
Hi there,
Q1.
<Before>
C = 1p + 864
B = 1p
<Process>
1/6 C sold = 1/6 of the 1p + 1/6 of 864
3/4 B sold = 3/4 of the 1p
LCM (lowest common multiple) of 6, 4 = 24
So 1p of C and B made up 24u each.
C sold = ( 1/6 x 24u ) + ( 1/6 x 864 ) = 4u + 144
B sold = ( 3/4 x 24u ) = 18u
<After>
C = ( 24u + 864 )  4u  144 = 20u + 720
B = 24u  18u = 6u
Given that difference left, C  B = 1728, we have ...
20u + 720  6u > 1728
14u > 1728  720 = 1008
1u > 1008 / 14 = 72
C ( at first ) = 1p + 864 = 24u + 864 > ( 24 x 72 ) + 864 = 2592
==========================================================
Q2.
<Before>
R = 1/7 = 1p
B = 6/7 = 6p
<Process>
Given that 1/3 R sold, we split the <Before> model for R, B into smaller equal units (u) by multiplying 3x.
So we have ...
R = 3u
B = 18u
Sold 1/3 R; Bought 1/2 as many B as before
<After>
R = 3u  1u = 2u
B = 18u + 9u = 27u
Given that there were 87 R and B in the end, we have ...
29u > 87
1u > 87 / 29 = 3
(a)
R ( end ) = 2u > 2 x 3 = 6
B ( end ) = 27u > 27 x 3 = 81
R : B ( end ) = 6 : 81 = 2 : 27
(b)
B ( at first ) = 18u > 18 x 3 = 54
===============================================
Trust the above solutions help.
Do not hesitate to clarify further , if any.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 627





By: Tping (offline) Tuesday, May 01 2012 @ 06:39 AM CDT



Tping 

Junior
Registered: 01/26/12 Posts: 25



