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 By: achieve_goal (offline)  Wednesday, May 30 2012 @ 02:40 AM CDT (Read 853 times)
achieve_goal

1. Mandy had some money. After spending \$31 on 5 notebooks & 8 files,she was short of \$0.40 if she were to buy another notebook. However she would have \$0.60 left if she were to buy one more file.

(a) How much did a notebook cost?

(b) How much money did Mandy have?

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

2.There were 800 people at a party. 3/8 of them were were women and the rest were men. After 1 hour, some men left the party and the number of men became 2/5 of the number of the remaining people. Another 15 mins later, some women left the party and the number of men remaining at the party was 5/7 of the number of people who were still at the party. How many people were still at the party?

//Pls help me. Thank u.

Regular Member

Registered: 09/14/11
Posts: 102

 By: echeewh (offline)  Thursday, May 31 2012 @ 09:18 PM CDT
echeewh

Hey there,

Following pls find the worked solutions:

Q1.

Note: **** - fillup/buffer whitespace for alignment purpose ( i.e. imagine *** as whitespace )

(a)

*****31.00 1N
<------------><----------------->
|---------------------------|<--->|
*************************0.40

|---------------------------|
<------------><---><--->
**31.00******1F 0.60

Applying Gap & Difference method, we have ...

1N - 1F = 1.00 --- (1)
5N + 8F = 31.00 --- (2)

As question is interested in N, we shall eliminate F in the following manner:

(1)x8: 8N - 8F = 8.00 ---(3)

Comparing (3) and (2),
(2) + (3):
5N + 8F + 8N - 8F = 31.00 + 8.00
13N = 39
1N = 39 ÷ 13 = \$3

(b)

Amt of money M had = 31 + 1N - 0.40
= 31 + 3 - 0.40 = \$33.60

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

Q2.

<Before>
W: (3/8) x 800 = 300
M: 800 - 300 = 500

<Process1>
1 hr later, some M left party (i.e. W remains same)

<After>
W: 300

Given that remaining M is 2/5 of remaining total, that means the 300 W remaining makes up 3/5 of remaining total.

We now have ...

3/5 = 300
5/5 = 300 ÷ (3/5) = 300 x (5/3) = 500

M = 2/5 = (2/5) x 500 = 200

We now have a new <Before> and <After> ratio as follows:

<Before>
W : M
300 : 200
3 : 2 --- (1)

<Process2>
15 mins later, some W left party and remaining M makes up 5/7 of remaining total. So the <After> ratio becomes...

<After>
2 : 5 --- (2)

Applying <Unchanged Qty/Item> concept (since number of M remains unchanged), we take lowest common multiple of 2 and 5, which is 10.

(1)x5:

<Before>
W : M
15 : 10 --- (3)

(2)x2:

<After>
4 : 10 --- (4)

At this stage, total number of W and M is 500. Hence, we have ...

15u + 10u --> 500
25u --> 500
1u --> 20

Number of people still remaining at party:
14u --> 14 x 20 = 280

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

Trust the above solution helps.. Do let me know again if it doesnt match the answerkey as these are not provided.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: achieve_goal (offline)  Sunday, June 03 2012 @ 03:42 AM CDT
achieve_goal

Hi there, thanks 4 ur help!

Regular Member

Registered: 09/14/11
Posts: 102

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