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Problem Solving Strategies_11/6/2012
A) Concept : Part-whole relationship
1. Jamine had some saving in the bank. She decided to spend 25% of her savings on cloths and the remaining amount on a television set and hi-fi in the ratio 2 : 3. She found that she had spent $280 more on the hi-fi set than on the clothes. How much was her original savings?
C : TV + HF
( 1 : 3 ) x5
( 2 : 3) x3
5 : 6 : 9 à 20 units
9units – 5 units = 4units
4 units = 280
1unit =70
20 units = 20 x 70 =1400
2) 24% of the beads in the box were red. There were 99 more yellow beads than red beads. The remaining 57 beads were green
a)How many beads were yellow?
b)What percentage of the beads in the box was green?
Red Yellow green
24% 24%+99 57
100% - 48% = 99 + 57 = 156
52% = 156 1% = 3
a) Y : 24 x 3 + 99 = 171
b)100% = 3 x 100 = 300
%tage of green beads 57/300=19/100 x 100 = 19%
3. Mr Cheng spent $1200 in some jewels and 55% of the remainder on a watch. He had 30% of his original amount of money left. Find the amount of money he had at first.
100% -->1200 (jewels)
--->100% - 1200
(Remainder) 55% (watch)
45% (30% original)
45% remainder 30% original
1% remainder 2/3% original
100% remainder 200/3% original
300/3 – 200/3 1200
100% 1200x3 = 3600
C) Concept - Equal Fraction
7. Helen and Jane went shopping with a total amount of $184. After Helen spent 1/3 of her money and Jane spent 4/7 of hers, they had the same amount of money left. How much money did Jane have at first?
2/3 -->6/9 (Helen) = 3/7--> 6/14 (Jane) (equal fraction, make the numerator equal in value)
9u+14u=23u
23u-->184 1u --> 8
Jane had 14x8 =$112 at first.
8. Some parents went to attend a creativity workshop, 2/5 of the number of mothers who attended was equal to 2 times the number of fathers. When another 12 fathers joined the workshop after the break and 45 mothers left, the ratio of the number of mothers to the number of fathers became 5 : 2.
(a) What was the ratio of the number of mothers to the number of fathers attending the workshop at first? Give your answer in its simplest form.
(b) Find the number of mothers in the workshop after the break.
Mothers Fathers
2/5 = 2/1
5u 1u
-45 +12
5 2
a) 5 : 1
Using cross multiplication,
5u-45 = 1u + 12
5 2 10u-90=5u+60
5u=150
1u=30
b) 5x30-45=105
9. There are more employee in ABC Bank than XYZ Bank. 30% of the employee in ABC Bank is 18 more than 40% of the employee in XYZ Bank. If 10% of the employee in ABC Bank quit to join XYZ, there will be 78 more employee in ABC Bank than XYZ Bank.
a)how many employee are there in XYZ Bank?
b)how many percent more employee are there in ABC Bank than XYZ Bank?
Leave your answer to the nearest whole number.
ABC XYZ
3/10 = 2/5+18 20u+60 15u
6/20=6/15+18 change -2u-6 +2u+6
1/20=1/15+3 18u+54 17u+6
20/20=20/15+60
18u + 54 - (17u + 6) = 78
1u+54-6=78, 1u=30
a) There are 15x30=450 employee in XYZ Bank
b) ABC Bank employees --> 20x30+60=660 , 660-450=210
210/450x100=47%
1. Jamine had some saving in the bank. She decided to spend 25% of her savings on cloths and the remaining amount on a television set and hi-fi in the ratio 2 : 3. She found that she had spent $280 more on the hi-fi set than on the clothes. How much was her original savings?
C : TV + HF
( 1 : 3 ) x5
( 2 : 3) x3
5 : 6 : 9 à 20 units
9units – 5 units = 4units
4 units = 280
1unit =70
20 units = 20 x 70 =1400
2) 24% of the beads in the box were red. There were 99 more yellow beads than red beads. The remaining 57 beads were green
a)How many beads were yellow?
b)What percentage of the beads in the box was green?
Red Yellow green
24% 24%+99 57
100% - 48% = 99 + 57 = 156
52% = 156 1% = 3
a) Y : 24 x 3 + 99 = 171
b)100% = 3 x 100 = 300
%tage of green beads 57/300=19/100 x 100 = 19%
3. Mr Cheng spent $1200 in some jewels and 55% of the remainder on a watch. He had 30% of his original amount of money left. Find the amount of money he had at first.
100% -->1200 (jewels)
--->100% - 1200
(Remainder) 55% (watch)
45% (30% original)
45% remainder 30% original
1% remainder 2/3% original
100% remainder 200/3% original
300/3 – 200/3 1200
100% 1200x3 = 3600
C) Concept - Equal Fraction
7. Helen and Jane went shopping with a total amount of $184. After Helen spent 1/3 of her money and Jane spent 4/7 of hers, they had the same amount of money left. How much money did Jane have at first?
2/3 -->6/9 (Helen) = 3/7--> 6/14 (Jane) (equal fraction, make the numerator equal in value)
9u+14u=23u
23u-->184 1u --> 8
Jane had 14x8 =$112 at first.
8. Some parents went to attend a creativity workshop, 2/5 of the number of mothers who attended was equal to 2 times the number of fathers. When another 12 fathers joined the workshop after the break and 45 mothers left, the ratio of the number of mothers to the number of fathers became 5 : 2.
(a) What was the ratio of the number of mothers to the number of fathers attending the workshop at first? Give your answer in its simplest form.
(b) Find the number of mothers in the workshop after the break.
Mothers Fathers
2/5 = 2/1
5u 1u
-45 +12
5 2
a) 5 : 1
Using cross multiplication,
5u-45 = 1u + 12
5 2 10u-90=5u+60
5u=150
1u=30
b) 5x30-45=105
9. There are more employee in ABC Bank than XYZ Bank. 30% of the employee in ABC Bank is 18 more than 40% of the employee in XYZ Bank. If 10% of the employee in ABC Bank quit to join XYZ, there will be 78 more employee in ABC Bank than XYZ Bank.
a)how many employee are there in XYZ Bank?
b)how many percent more employee are there in ABC Bank than XYZ Bank?
Leave your answer to the nearest whole number.
ABC XYZ
3/10 = 2/5+18 20u+60 15u
6/20=6/15+18 change -2u-6 +2u+6
1/20=1/15+3 18u+54 17u+6
20/20=20/15+60
18u + 54 - (17u + 6) = 78
1u+54-6=78, 1u=30
a) There are 15x30=450 employee in XYZ Bank
b) ABC Bank employees --> 20x30+60=660 , 660-450=210
210/450x100=47%
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