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 Maths Help for my daughter
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By: AngelLim (offline)  Tuesday, October 23 2012 @ 03:26 AM CDT (Read 1198 times)  
AngelLim

Hi everyone.
I am new to this forum and I would like to ask help for some Maths questions for my daughter who is having her Maths exam next Monday. Here are the questions. I would appreciate it if you can reply ASAP. Thanks in advance.

Q1. There are some pens and pencils in a box. 2/3 of the number of pens is equal to 3/5 of the number of pencils. If there were 15 fewer pens than pencils, what was the total number of pens and pencils in the box?

Q2. Isabella spent $897 on entertainment and food and 0.25 of the remainder on clothes. If she had 3/7 of her salary left, how much is her salary?

Q3. If Chris gives Ben 8 stickers, they will have the same amount of stickers each. If Ben gives Chris 8 stickers, Chris will have 5 times as many stickers as Ben.

a) How many stickers does Chris have?
b) Express the number of stickers Ben has as a fraction of the number of stickers Chris has. Leave your answer in simplest form.

Q4. There were some sweets in Boxes X, Y and Z. Box X contained 1/5 of the total number of sweets in X, Y and Z. The number of sweets in Y was twice the total number of sweets in X and Z. If there were 32 more sweets in Box Y than in Box Z, find the total number of sweets in the 3 boxes.

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By: echeewh (offline)  Tuesday, October 23 2012 @ 04:20 AM CDT  
echeewh

Hey Angel,

Following pls find my worked solutions: ( Will complete remaining by tomorrow Smile )

Q1.


P=Pens; C=Pencils

Apply <Equal Concept> - make numerator of the 2 fractions to be same; then denominator will be the starting/initial number of units of respective object/subject.

(2/3)P = (3/5)C
(2/3) × (3/3) P = (3/5) × (2/2) C
(6/9)P = (6/10)C

Hence, P = 9u; C = 10u

Given there were 15 fewer pens than pencils, we have ..

C - P = 15
10u - 9u --> 15
1u --> 15

Total number of P, C = 9u + 10u = 19u --> 19 × 15 = 285

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

Q2

*** - for alignment purpose

********<------ E & F ---->< C ><---- 3/7total ----->
Salary |<----- 897 ------->|-------|-------|-------|-------|
****************************< 1u><-------- 3u -------->

3u --> (3/7) total
1u --> (1/7) total

Hence, E & F = (3/7) total --> 897
Salary = (7/7) total --> 897 ÷ (3/7) = 897 × (7/3)
= $2093

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

Trust these help.

Do let me know again if these are different from your Answerkey or if there's further clarification.

Cheers and all the best to ur gal,
Edward

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Posts: 623

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By: ystella (offline)  Tuesday, October 23 2012 @ 09:34 AM CDT  
ystella

Hi Angel,

Q3,
first scenario
C [----][----][ ][ -8 ]
B [----][----][+8]

second scenario
C [ ][ ][ ][ ][+8 ]
B [ ][ -8]

a) Chris has 32 stickers
b) 16/32 = 1/2

Hope this help.

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Registered: 04/03/09
Posts: 5

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By: echeewh (offline)  Tuesday, October 23 2012 @ 08:11 PM CDT  
echeewh

Hey Angel,

As promised,

Following pls find my worked solutions to Q3 and Q4.

*** - for alignment purpose

Q3.

<after>

B |-------------------|
C |-------------------|

<process>
Apply <work backwards> method,
B: -8
C: +8

<Before>

B |------------|<-8->
C |------------------<-8->|

<process>
B: -8
C: +8

<after>

**<1u>
B |-----|<-8->
C |-----------<----16----><-8->|
**<------------- 5u -------------->

Apply <Gap & Difference> method, we have ...

5u - 1u --> 8 + 16 + 8 = 32
4u --> 32
1u --> 32 ÷ 4 = 8

(a)

C (at first) = 5u - 8 --> (5 × 8) - 8
= 40 - 8 = 32

(b)

B (at first) = 1u + 8 --> 8 + 8 = 16
(B / C) = 16/32 = 1/2

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

Q4.

X : (Y + Z) Total
1 : ** 4 ***** 5 -- (1)

Y : (X + Z) Total
2 : ** 1 ***** 3 -- (2)

Since total number of sweets in X,Y,Z remain unchanged in the two ratios above <Unchanged Total>,
multiply (1) x 3; (2) x 5 ( common multiple) as follows:

(1)x3:

X : (Y + Z) Total
3 : ** 12 *** 15

(2)x5:

Y : (X + Z) Total
10 : ** 5 **** 15

So, X = 3u; Y = 10u; Z = 5u - 3u = 2u

If there were 32 more sweets in Box Y than in Box Z,

Y - Z = 32
10u - 2u --> 32
8u --> 32
1u --> 4

Total sweets in X,Y,Z = 3u + 10u + 2u = 15u

15u --> 15 × 4 = 60

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

Trust the above helps.

Do let me know again if these answers are different from your Answerkey or if there's further clarification.

Cheers,
Edward

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Registered: 04/21/11
Posts: 623

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