Tuesday, June 26, 2012
Wednesday, June 20, 2012
Friday, June 15, 2012
Thursday, June 14, 2012
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%
Tuesday, September 7, 2010
September homework - Geometry
Q1. (1)
Q2. (2)
Q3. (3)
Q4. angle x = 149 degree
Q5. angle z = 45 degree (alternate angle)
Q6. angle a = 40 degree (angle on a straight line and isoscellis triangle)
Q7. Find Angle XYZ
Angle XYZ = 180 - 20 -20 -30 -30 = 80
(sum of angles on a straight line =180)
Q2. (2)
Q3. (3)
Q4. angle x = 149 degree
Q5. angle z = 45 degree (alternate angle)
Q6. angle a = 40 degree (angle on a straight line and isoscellis triangle)
Q7. Find Angle XYZ
Angle XYZ = 180 - 20 -20 -30 -30 = 80
(sum of angles on a straight line =180)
Friday, July 23, 2010
iMaths Practise 3
1. There are 1500 pupils in upper primary in ABC school. 1/4 of the boys and 2/3 of the girls are in lower primary. 60% of the upper primary pupils are boys while the rest are the upper primary girls.
(a) What is the ratio of the total no. of boys to the total no. of girls in the school? (Express your answer in the simplest form)
(b) 900 girls in the lower primary do not wear spectacles. Of all the lower primary pupils, what is the percentage of girls who wears spectacles?
2. Peter has $8 more than Ben. Then, Peter gave 1/4 of his money to Ben. As a result, the ratio of the amount of money Peter had to the amount of money Ben became 5:7. How much money did Peter give to Ben?
3. Harry spent 1/2 of his money on some muffins and 3/5 of his remaining money on 5 pieces of cakes. Each piece of cake cost thrice as much as muffins. How many muffins did he buy?
4. The ratio of Xavier’s savings to Henry’s savings was 6:7.
Xavier and Henry shared the cost of a game set in the ratio 4:5 respectively
Xavier used 2/3 of his saving to pay for his share of the game set. Henry was left with $150 after paying for his share.
a) What was Henry's saving’s before paying for his share of the game set?
b) What was the cost of the game set?
5. There are 160 red marbles and some blue marbles in a box. If 3/8 of the blue marbles is taken out of the box and 50 new red marbles are put into the box, the ratio of the number of red marbles to the number of
blue marbles becomes 7:9. How many blue marbles are there in the box?
*6. A boutique owner bought 1.5 times as many skirts as dresses. She spent $1496 altogether. A dress costs $4 more than a skirt. The total cost of the skirts was $136 more than the total cost of the dresses. Find the cost of 2 skirts and 1 dress.
(a) What is the ratio of the total no. of boys to the total no. of girls in the school? (Express your answer in the simplest form)
(b) 900 girls in the lower primary do not wear spectacles. Of all the lower primary pupils, what is the percentage of girls who wears spectacles?
2. Peter has $8 more than Ben. Then, Peter gave 1/4 of his money to Ben. As a result, the ratio of the amount of money Peter had to the amount of money Ben became 5:7. How much money did Peter give to Ben?
3. Harry spent 1/2 of his money on some muffins and 3/5 of his remaining money on 5 pieces of cakes. Each piece of cake cost thrice as much as muffins. How many muffins did he buy?
4. The ratio of Xavier’s savings to Henry’s savings was 6:7.
Xavier and Henry shared the cost of a game set in the ratio 4:5 respectively
Xavier used 2/3 of his saving to pay for his share of the game set. Henry was left with $150 after paying for his share.
a) What was Henry's saving’s before paying for his share of the game set?
b) What was the cost of the game set?
5. There are 160 red marbles and some blue marbles in a box. If 3/8 of the blue marbles is taken out of the box and 50 new red marbles are put into the box, the ratio of the number of red marbles to the number of
blue marbles becomes 7:9. How many blue marbles are there in the box?
*6. A boutique owner bought 1.5 times as many skirts as dresses. She spent $1496 altogether. A dress costs $4 more than a skirt. The total cost of the skirts was $136 more than the total cost of the dresses. Find the cost of 2 skirts and 1 dress.
iMaths Practise 2 Solution
Q1. Case 1
X = unit + 30
Y = unit - 30
Case 2
X = unit + 30 + 18
Y = unit - 30 - 18
unit+30+18 = 4(unit-30-18)
unit+48 = 4units-192
3 units = 240
1 unit = 80
At first, X = unit+30 = 80+30=110
At first,number of beads in Box X was 110.
Q2. In the end, all 3 containers became equal.
So, P=Q=E = 162 divided by 3 = 54
R(Original) = 54 divided by 3 = 18
Q(Before giving R and after receiving from P)= 54+18x2 = 90
Q(Original) = 90 divided by 3 = 30
P(Original) = 54+30x2 = 114
Number of buttons in container P at first = 114.
Q3. In the end,
X = 115
Y = 90
2/3 of Y = 90
Y = 135
X = 115-(90÷2)=70
2/3 of X = 70
X = 70x3/2= 105
Y = 135-(70÷2) = 100
4/5 of Y = 100
Y = 125
X = 105-(100÷4) = 80
AT first, there were 80 marbles in Box X and 125 marbles in Box Y.
Q4. (7+½)x2=15
(15÷2)+½ = 8
Number of chocolate bars that the third child got = 8.
Note
1st child got 32 chocolate bars
2nd child got 16 chocolate bars
3rd child got 8 chocolate bars
4th child got 7 chocolate bars
Total = 63 chocolate bars.
Q5. Women = 1/5
Men + Children = 4/5
Men = 2/5x4/5 = 8/25
Children = 1-1/5-8/25 = 12/25
12/25 of total = 266+266x2 = 798
8/25 of total = 532
Number of men in the hall = 532.
Q6. Cloths = 5/9
Gifts = 1/3
Mother + Left = 1-5/9-1/3 = 1/9
1/9 of the total = $1500+$560 = $2060
Total for Samuel= $2060x9 = $18540
Total for Samuel and Nigel = ($18540/4)x9 = $41715
Q7. 3N + J = 40.80
2N + 2J = 45.20 (86 - 40.80)
J - N = 4.4
Rewriting N as J -4.4
3J - 13.20 + J = 40.80, J = 54/3 = 13.50
Q8. 0.7 blue + 0.7 red --> 91 (adding both)
7 blue + 7 red --> 910 (times by 10)
1 blue + 1 red --> 130 (divide by 7)
X = unit + 30
Y = unit - 30
Case 2
X = unit + 30 + 18
Y = unit - 30 - 18
unit+30+18 = 4(unit-30-18)
unit+48 = 4units-192
3 units = 240
1 unit = 80
At first, X = unit+30 = 80+30=110
At first,number of beads in Box X was 110.
Q2. In the end, all 3 containers became equal.
So, P=Q=E = 162 divided by 3 = 54
R(Original) = 54 divided by 3 = 18
Q(Before giving R and after receiving from P)= 54+18x2 = 90
Q(Original) = 90 divided by 3 = 30
P(Original) = 54+30x2 = 114
Number of buttons in container P at first = 114.
Q3. In the end,
X = 115
Y = 90
2/3 of Y = 90
Y = 135
X = 115-(90÷2)=70
2/3 of X = 70
X = 70x3/2= 105
Y = 135-(70÷2) = 100
4/5 of Y = 100
Y = 125
X = 105-(100÷4) = 80
AT first, there were 80 marbles in Box X and 125 marbles in Box Y.
Q4. (7+½)x2=15
(15÷2)+½ = 8
Number of chocolate bars that the third child got = 8.
Note
1st child got 32 chocolate bars
2nd child got 16 chocolate bars
3rd child got 8 chocolate bars
4th child got 7 chocolate bars
Total = 63 chocolate bars.
Q5. Women = 1/5
Men + Children = 4/5
Men = 2/5x4/5 = 8/25
Children = 1-1/5-8/25 = 12/25
12/25 of total = 266+266x2 = 798
8/25 of total = 532
Number of men in the hall = 532.
Q6. Cloths = 5/9
Gifts = 1/3
Mother + Left = 1-5/9-1/3 = 1/9
1/9 of the total = $1500+$560 = $2060
Total for Samuel= $2060x9 = $18540
Total for Samuel and Nigel = ($18540/4)x9 = $41715
Q7. 3N + J = 40.80
2N + 2J = 45.20 (86 - 40.80)
J - N = 4.4
Rewriting N as J -4.4
3J - 13.20 + J = 40.80, J = 54/3 = 13.50
Q8. 0.7 blue + 0.7 red --> 91 (adding both)
7 blue + 7 red --> 910 (times by 10)
1 blue + 1 red --> 130 (divide by 7)
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