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 P5 Maths 2011 SA2 Catholic High Paper 2 Q9 & Q14
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By: geniuskids (offline)  Monday, October 15 2012 @ 10:21 PM CDT (Read 836 times)  
geniuskids

Help needed urgently:-

Q9 : Sean had twice as much money as his brother, George. After George spent $20 and Sean received another $50 from their mother, Sean had five times as much money as George. How much money did Sean have at first?

Answer is 100

Q14 : Aaron and Ben shared a sum of $200. Aaron gave 3/5 of what he has to Ben. Ben later gave 1/5 of what he has back to Aaron. They ended up with equal amount amount of money. How much did Aaron have at first?

Answer is $187.50


Thanks

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By: echeewh (offline)  Friday, October 19 2012 @ 11:26 PM CDT  
echeewh

hey there,

Following pls find my worked solutions:

Q9

<Before>
S |-----------------------|
G |------------|

<Process>
S: +50
G: -20

<After>

**<------------- 5u ------------->
S |-----------------------|<- 50 ->|
G |----|<20>
**<1u> <1u+20>


Apply <Gap & Difference> method,

5u - 2u --> 20 + 20 + 50
3u --> 90
1u --> 30

S (at first) = 5u - 50 --> (5 × 30) - 50
= 150 - 50
= 100


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

Q14

Apply <work backwards> method starting from the point

where both A,B had equal amounts.

<After>

B gave (1/5) to A, so B left with (4/5) or 4 parts. Hence, split B into 4 equal parts (p). Likewise, A = 4p.


A |--|--|--|--|
B |--|--|--|--|


<process>

A: - 1p
B: + 1p

<Before>

A |--|--|--| --> 3p
B |--|--|--|--|--| --> 5p

<Before1>

A gave (3/5) to B, so A left with (2/5) or 2 units (u). Hence, multiply A by 2x --> 3p × 2 --> 6u.
Likewise, multiply B by 2x --> 5p × 2 --> 10u.

A: (2/5) --> 6u
(5/5) --> 6u × (5/2) = 15u

A: + 9u
B: - 9u

A |-|-|-|-|-|-|-|-|-|-|-|-|-|-|-| --> 15u
B |-| --> 1u

Given that A,B shared $200 at first,

A + B = 200
15u + 1u --> 200
16u --> 200
1u --> 200 ÷ 16 = 12.50

A (at first) = 15u --> 15 × 12.50 = $187.50

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

Trust the above helps.

Do let me know again if there's further clarification.

Cheers,
Edward

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By: geniuskids (offline)  Saturday, October 20 2012 @ 04:06 AM CDT  
geniuskids

Thanks again Edward, managed to handle these!.

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