
By: Jlen (offline) Saturday, February 22 2014 @ 03:13 AM CST (Read 2233 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

Newbie
Registered: 05/05/13 Posts: 10





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

Active Member
Registered: 04/21/11 Posts: 627





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

Active Member
Registered: 04/21/11 Posts: 627





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

Newbie
Registered: 05/05/13 Posts: 10





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

Regular Member
Registered: 03/20/12 Posts: 111





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



echeewh 
Hey <Jlen>,
You are most welcome.
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.

Active Member
Registered: 04/21/11 Posts: 627



