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 By: achieve_goal (offline)  Monday, June 17 2013 @ 08:44 PM CDT (Read 1258 times)
achieve_goal

There are more pupils in School A than School B. 30% of the pupils 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 as fraction in the simplest form.

Regular Member

Registered: 09/14/11
Posts: 102

 By: echeewh (offline)  Monday, June 17 2013 @ 10:26 PM CDT
echeewh

Hi <achieve_goal>,

Following pls find my worked solution:

<before>

(3/10)A - (4/10)B = 45 -- (1)
(3/10)A = (4/10)B + 45
(1/10)A = (4/30)B + 15

<after>
B:
1B + (4/30)B + 15 = (34/30)B + 15 = (17/15)B + 15

(9/10)A - (17/15)B - 15 = 200
(9/10)A - (17/15)B = 215 -- (2)

(a)
Using Simultaneous method and eliminate A:

(1)x3:
(9/10)A - (12/10)B = 135 -- (3)

(2)-(3):
(12/10)B - (17/15)B = 80
(6/5)B - (17/15)B = 80
(1/15)B = 80
B = 80 × 15 = 1200

(b)
in (1),
(3/10)A - (4/10)B = 45
(3/10)A = 45 + (4/10)B = 45 + 480 = 525
A = 525 × (10/3) = 1750

%less = [(B - A) / A] × 100
[(1200 - 1750) / 1750] × 100
= - 31 3/7 %

School B has 31 3/7 % less pupils than School A

======

Trust this helps.

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

Cheers,
Edward

P/s. Afraid you are not making much progress with this kind of skill yet.

Active Member

Registered: 04/21/11
Posts: 627

 By: achieve_goal (offline)  Tuesday, June 18 2013 @ 08:05 PM CDT
achieve_goal

Hey there,
I do not understand this part :
(2)-(3):
(12/10)B - (17/15)B = 80
(6/5)B - (17/15)B = 80
(1/15)B = 80
B = 80 × 15 = 1200

Can you kindly help me with that part?

Regular Member

Registered: 09/14/11
Posts: 102

 By: echeewh (offline)  Tuesday, June 18 2013 @ 09:45 PM CDT
echeewh

Hi <achieve_goal>,

Here's the clarification bit :

(2)-(3) means taking the difference between the two equations.

(9/10)A - (17/15)B - (9/10)A + (12/10)B = 215 - 135
(12/10)B - (17/15)B = 80

Simplifying (12/10)B gives (6/5)B, so

(6/5)B - (17/15)B = 80

and I'm very sure you can work out the rest on your own.

=======

Trust this clarifies.

Let me know again if you are in doubt still.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: achieve_goal (offline)  Tuesday, June 18 2013 @ 10:48 PM CDT
achieve_goal

Thank you for clarifying; I understand better now.

Regular Member

Registered: 09/14/11
Posts: 102

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