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By: KCTAN (offline)  Saturday, August 03 2013 @ 03:07 AM CDT (Read 1062 times)  
KCTAN

Hi,

Can anyone help with the following questions? Thank you!

1. Roy had 50 marbles than Jude. Roy gave 60% of his marbles to Jude.
Jude then gave 50% of his marbles to Roy.
In the end, Jude had 160 fewer marbles than Roy.
How many did Roy have at first?

2. There are more pupils in School A then School B.
30% in School A is 45 more than 40% of the pupils in School B.
If 10% of the pupils in School A leaves to join School B, there will be 200 more pupils in School A than School B.

(a) How many pupils are there in School B?
(b) How many percent less pupils are there in School B than School A?
(Leave your answer in simplest form.)

(3) In a school hall, chairs were arranged in rows such that there were exactly 9 chairs in each row,
For a concert, Mr Ong brought 6 more chairs into the school hall and rearranged the chairs.
There are now exactly 7 chairs in each row and 12 more rows than before.

How many chairs are there in the school hall for the concert?

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By: echeewh (offline)  Saturday, August 03 2013 @ 09:54 PM CDT  
echeewh

Hey <KCTAN>,

//updated
Q1 completed and posted 5/8/13 , 9am
//


Q1 is still in progress. Noted some missing word(s) in this 1st line ( Roy had 50 marbles than Jude )

As for Q2, pls refer to the solution provided on p6 of this forum (as at 4/8/13) [ Subject: maths , last posted on 18/6/13 ]. Thank you.

Following is my worked solution for Q3:

Q3

<before>
Let number of rows be 1u.

Given that there were 9 chairs in each row,
Total chairs = 9u

<after 6 more chairs added>

Total chairs = 9u + 6 -- (1)

Number of rows = 1u + 12

Given that there were 7 chairs in each row,
Total chairs = 7 × (1u + 12) = 7u + 84 -- (2)

Hence, we can equate (1),(2) {i.e. (1) = (2)}

9u + 6 = 7u + 84
9u - 7u = 84 - 6
2u = 78
1u = 39

Number of chairs for the concert
= 9u + 6
= (9 × 39) + 6
= 351 + 6
= 357

==========

Trust this helps.

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,
Edward

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By: echeewh (offline)  Sunday, August 04 2013 @ 07:57 PM CDT  
echeewh

Hi there,

Following is the worked solution for Q1.

*** - for alignment purpose

Assume the statement is "Roy had 50 marbles more than Jude"

R - J = 50

<after R gave 60% (3/5) to J>

Develop the <before> model as follows:
Split the equal portion of R, J into 5 equal units as shown:

<Before>

R |--|--|--|--|--|<50>| --> 5u + 50
J |--|--|--|--|--| ******* --> 5u

<R gave (3/5) to J>

(3/5)R = (3/5) × (5u + 50)
= 3u + 30

<after>

R: 5u + 50 - 3u - 30 = 2u + 20
J: 5u + 3u + 30 = 8u + 30

<after J gave 50% to R>

50% J = (1/2)J
= (1/2) × (8u + 30)
= 4u + 15

R: 2u + 20 + 4u + 15 = 6u + 35
J: 8u + 30 - 4u - 15 = 4u + 15

Given that J had 160 fewer marbles than R in the end,

R - J = 160
6u + 35 - 4u - 15 = 160
2u + 20 = 160
2u = 160 - 20 = 140
1u --> 140 ÷ 2 = 70

R (at first) = 5u + 50
5u + 50 --> (5 × 70) + 50
= 350 + 50
= 400

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

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By: KCTAN (offline)  Sunday, August 04 2013 @ 11:02 PM CDT  
KCTAN

Hi echeewh,

Thank you so much for the explanation.
The answers are correct.
Apologies for the typo, I left out the word "more".
The correct statement is indeed "Roy had 50 marbles more than Jude".

Appreciate your guidance! Smile


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