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 Pls help on these questions
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By: Jlen (offline)  Saturday, February 22 2014 @ 03:13 AM CST (Read 2221 times)  
Jlen

Hi all,

I don't have answer for these sums.
Pls help

1. 25% of Mr. Tan's salary was $250 more than 1/5 of Mr.Lim's salary. After Mr. Tan spent
60% of his salary and Mr.Lim spent 1/2 of his salary, Mr. Tan had $22 more than Mr.Lim.
What was Mr. Tan's salary?

2. Mr.Tan and Mr. Lim had a combined salary of $5400 altogether. After Mr Tan spent 2/5 of
his salary and Mr.Lim spent 3/4 of his salary, Mr. Tan had $1200 more than Mr.Lim.
What was Mr.Tan's salary?

3. A fruit seller had 228 jack fruits and mangosteens. After he sold 2/3 of the jack fruits and 2/5 of the
Mangosteens, he had 36 more mangosteens than jack fruits left.how many fruits had he left?

4. A group of 375 pupils were at a concert. After 3/4 of the boys and 3/5 of the girls left the concert,
There were 120 boys and girls who remained at the concert. How many boys were at the concert
at first ?

Thanks in advance for your help.
Regards,
Jlen

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By: echeewh (offline)  Saturday, February 22 2014 @ 07:53 PM CST  
echeewh

Hey <Jlen>

The following questions can be solved using either <Work Backward> method or <Simultaneous> method.

Q3 and Q4 will be posted in due course.

Following are my worked solutions (using <Work Backward> method:

Q1.

<After>

T |---------< 22 >|
L |---------|

Using <Work Backward> method and after T spent 60% (3/5) of salary, T was left with (2/5) salary. So split the equal portions of T and L into 2 equal units each.

T |----|----< 22 >| --> 2u + 22
L |----|----| --> 2u

<Before>

T:
(2/5)T = 2u + 22
(1/5)T = 1u + 11
(5/5)T = 5u + 55

L:
(1/2)L = 2u
(2/2)L = 4u

Given that 25% (1/4) of Mr. Tan's salary (T) was $250 more than 1/5 of Mr.Lim's salary (L), we have ...

(1/4)T - (1/5)L = 250
(1/4)(5u + 55) - (1/5)(4u) = 250

Common multiple of 4,5 is 20. So multiply the above equation 20x, giving ...

[5 × (5u + 55)] - [4 × 4u] = 5000
25u + 275 - 16u = 5000
9u --> 5000 - 275 = 4725
1u --> 4725 ÷ 9 = 525

Hence, salary (T) = 5u + 55
5u + 55 --> (5 × 525) + 55 = $2680

=========

Q2.

<After>

T |--------< 1200 >|
L |--------|

Using <Work Backward> method and after T spent (2/5) of salary, T was left with (3/5) salary. So split the equal portions of T and L into 3 equal units each.

T |--|--|--< 1200 >| --> 3u + 1200
L |--|--|--| --> 3u

<Before>

T:
(3/5)T = 3u + 1200
(1/5)T = 1u + 400
(5/5)T = 5u + 2000

L:
(1/4)L = 3u
(4/4)L = 12u

Given that Mr.Tan (T) and Mr. Lim (L) had a combined salary of $5400 altogether, we have ...

T + L = 5400
5u + 2000 + 12u = 5400
17u --> 5400 - 2000 = 3400
1u --> 3400 ÷ 17 = 200

Hence, Salary (T) = 5u + 2000
5u + 2000 --> (5 × 200) + 2000 = $3000

=========

Trust these help.

Do let me know again if there are further clarifications.

Cheers,
Edward


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By: echeewh (offline)  Sunday, February 23 2014 @ 04:32 PM CST  
echeewh

Q3 and Q4 are solved using the <Simultaneous> method as shown:

Apply <Simultaneous> method, we have ...

J + M = 228 -- (1)
(3/5)M - (1/3)J = 36 -- (2)

Common multiple of 5,3 is 15. So ...

(2)x15:
9M - 5J = 540 -- (3)

Comparing (1),(3), eliminate J.

(1)x5:
5J + 5M = 1140 -- (4)

(3)+(4):
9M + 5M = 540 + 1140
14M --> 1680
M --> 1680 ÷ 14 = 120

J = 228 - M
= 228 - 120
= 108

Total fruits left:
(1/3)J = (1/3) × 108 = 36
(3/5)M = (3/5) × 120 = 72

36 + 72 = 108

=========

Apply <Simultaneous> method, we have ...

B + G = 375 -- (1)
(1/4)B + (2/5)G = 120 -- (2)

Common multiple of 4,5 is 20. So ...

(2)x20:
5B + 8G = 2400 -- (3)

Comparing (1),(3), eliminate G.

(1)x8:
8B + 8G = 3000 -- (4)

(4)-(3):
8B - 5B = 3000 - 2400
3B --> 600
B --> 600 ÷ 3 = 200

==========

Trust these help.

Do let me know again if there are further clarifications.

Cheers,
Edward

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By: Jlen (offline)  Monday, March 10 2014 @ 09:08 AM CDT  
Jlen

Thanks Edward for the solutions.
Pls help with the below question as I am unable to open a new topic.

Kenny always spends 80% of his allowance and saves the rest.
If he increases his spending by 10%, his spending will increase by $16.
How much is Kenny's allowance ?

Answer: $200

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By: jo sarah (offline)  Monday, March 10 2014 @ 09:25 AM CDT  
jo sarah

Kenny always spends 80% of his allowance and saves the rest.
If he increases his spending by 10%, his spending will increase by $16.
How much is Kenny's allowance ?

Solution:

He spends 80% of his allowance at first.
then he increases his spending by 10%, this has to be of his spending (80% of allowance)
that means he spending is now:
110% x 80% = (110/100) x 80% = 88%
So that the increase is 8% of his allowance, and it is $16

His total allowance is $(16/8) x 100 = $200

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By: echeewh (offline)  Tuesday, March 11 2014 @ 06:14 PM CDT  
echeewh

Hey <Jlen>,

You are most welcome. Smile

Here's a slightly different flavour of my worked solution.

100% spending = 80% allowance
10% spending = (80 ÷ 100) × 10 = 8% allowance

Given that 10% spending = $16,

8% allowance = $16
100% allowance = (16 ÷ 8) × 100 = $200

Hence, Kenny's allowance is $200

=======

Trust this helps.

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

Cheers,
Edward.

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