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 By: Tping (offline)  Tuesday, May 01 2012 @ 12:48 AM CDT (Read 1543 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

Thank alot, Edward~

Junior

Registered: 01/26/12
Posts: 25

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