Mary had some $5 and $10 notes in her wallet. There was a total of 60 pieces of notes at first. She used half of the number of $5 notes and received another twelve $10 notes from her mother. After that, the number of $10 notes she had was 2/3 of the remaining number of $5 notes she had left. How much money did she have at first?
Solution
After she used half of her $5 notes and mother gave her twelve $10 notes:
8 units - 12 ---- 60
8 units ---- 60 – 12 = 72
1 unit ---- 72 divided by 8 = 9
($5 notes) 6 units ---- 6 x 9 = 54
($10 notes) 2 units – 12 = (2 x 9) – 12 = 6
She had -----
(54 x $5) + (6 x $10)
= $270 + $60
= $330 (Answer)
Sunday, August 30, 2009
Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q47
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A bus was rented at a fixed cost.The rental cost was split by a group of 60 people.When 10 people joined the group,the rental cost of the bus did not change but the charge for each person was $8.95 less than before.Find the cost of renting the bus
Adam gave Eve a ride from town a and travelled towards town b at 80km/h.when they were 5km from town b,adam dropped eve off.eve continued to walk at a speed of 4km/h towards town b.Adam then turned back to pick his daughter up in town a and headed for town b again at the same speed.Adam and eve reached town b at the same time.What was the distance between town a from town b? 5/4=1.25 5/80=0.0625 1.25-0.0625=1.1875 1.1875x80=95 95/2=47.5 47.5+5=52.5
173 sweets are to be given to 8 kids in as fair a manner as possible. what is the maximum number of sweets a kid can get?
In a class, there are 4 more boys than girls. 1/3 of the girls and 7/11 of the boys take the MRT train to school. If ½ of the class take the MRT, how many boys and girls are there in the class?
Girls -> 33 units
Boys -> 33 units + 4
1/3 x G = 1/3 x(33 units) = 11 units
7/11 x B = 7/11 x(33 units +4)= 21 units + 28/11
G/3 + 7B/11 = 11u + 21u + 28/11 = 32u + 28/11
Total of boys and girls in the class-> 2(32u +28/11)
= 64u + 56/11
64u + 56/11 = 33u + 33u + 4
64u + 56/11 = 66u + 4
2u = 12/11
u = 6/11
Girls -> 33u = 33 x 6/11 = 18
Boys -> Girls + 4 = 18+4 = 22
There are 22 boys and 18 girls in the class.
The ratio of the number of 50 cent coins to the number of 10 cent coins in a box was 5:3. 5-50 cent coins were taken out and exchanged for 10 cent coins of equal value. The money was then put back into the box. The ratio of 50 cent coins to 10 cent coins became 1:2. (a).How much money was there in the box?
(b).If 10 10cent coins were taken out and exchanged for 20cent coins and the money returned to the box, what would the ratio of the number of 10 cent coins to the number of 20 cent coins to the number of 50 cent coins be then? Give your answer in the simplest form.
At first - ratio:
50-cent coins : 10-cent coins
5 : 3
5 each of 50-cent coins were exchanged for 10-cent coins of equal value.
Value of 5 each of 50-cent coins = 5 x 0.50 = $ 2.50
Number of 10-cent coins = 2.50/0.10 = 25.
Later - ratio :
50-cent coins : 10-cent coins
1 : 2
For 50-cent coins, 5u-5=p - (1)
For 10-cent coins, 3u+25 = 2p - (2)
(1)x2
10u-10 = 2p - (3)
(3)-(2)
7u = 35
u = 5
Number of 50-cent coins-> 5u = 5 x 5 = 25.
Number of 10-cent coins-> 3u = 3 x 5 = 15.
Value of 50-cent coins->25x0.5 = $12.50
Value of 10-cent coins->15 x 0.1 = $ 1.50
(a)Amount of money in the box was $(12.50+1.50) = $ 14.00
(b)
Number of 50-cent coins ->5u-5 = 5(5)-5 = 20
Number of 10-cent coins ->2p = 2(20) = 40
10 each of 10-cent coins exchanged for equal value of 20-cent coins.
Value of 10 each of 10-cent coins-> 10 x 0.10 = $ 1.00.
Number of 20-cent coins that were exchanged -> 1.00/0.20 = 5.
Remaining number of coins:
50-cent coins -> 20
20-cent coins -> 5
10-cent coins -> 30
Ratio of the number of 10-cent coins to the number of 20-cent coins to the number of 50-cent coins would be
30 : 5 : 20
= 6 : 1 : 4 (in simplest form)
In a bag, the number of ten-cent coins was 2/5 of the number of twenty-cent coins. Gordon took out 10 twenty-cent coins from the bag. After exchanging them for ten-cents of equal value, he put the ten-cent coins into the bag. The number of twenty-cent coins then became 5/8 of the number of ten-cent coins. How much money was there in the bag?
Before (in terms of number)
10-cent coins : 20-cent coins
2 : 5
10 each of 20-cent coins exchanged for 20 each of 10-cent coins
After (in terms of number)
10-cent coins : 20-cent coins
8 : 5
5u-10/2u+20 = 5/8
10u+100 = 40u-80
30u = 180
u = 6
2u = 12 (10-cent coins)
5u = 30 (20-cent coins)
Amount of money in the bag was (12x10) + (30x20) = 720 cents = $ 7.20
On the first day of a camp, there were 540 more boys than girls. On the second day, 20% of the boys left the camp and the number of girls increased by 10%. If there were 2047 students at the end of the second day, how many students were there at the camp on the first day?
Girls-> unit
Boys -> unit + 540
20% of the boys left and number of girls increased by 10% ->
0.8(unit+540)+ 1.1unit remained on the second day.
0.8unit + 432 +1.1unit = 2047
1.9unit = 1615
1 unit = 850
Girls -> 850
Boys -> 850+540 = 1390
Number of students at the camp on the first day-> 850+1390 = 2240
Alice, Betty and Charloote had total of 640 marbles at first. The ratio of Betty's marbles to Charlotte's marbles was 5:4. After Alice and Betty each had lost 50% of their marbles, the three girls had 440 marbles left. How many marbles did Alice have at first?
A + B + C = 640
A/2 + B/2 + C = 440
A/2 + B/2 = 200
A + B = 400
C = 240
B = 5/4 x 240 = 300
A = 640-240-300 = 100
At first, Alice had 100 marbles.
Bryan and Tom were travelling in the same directoin from Town P to Town Q at different speeds. Both did not change their speeds throughout their journeys. Tom started his journey earlier than Bryan at an average of 60 km/h. Bryan passed Tom after travelling 3/8 of the journey. 5/1/2 hours later, when Bryan reached Town Q, Tom was 30km away from Town Q. Find the time taken by Tom to travel from Town P to Town Q.
5/8 of the total journey =(5.5 x 60) + 30 = 360 km.
3/8 of the total journey = 360/5 x 3 = 216 km
Time taken (Tom) from Town P to where they met = 216/60 = 3 h 36 min
Time taken for Tom to travel remaining 30 km = 30/60 = 1/2 h
Total time taken for Tom to travel from Town P to Town Q = 3 h 36 min + 30 min + 5 h 30 min = 9 h 36 min.
Mrs Tan had a sum of money to spend. She spent 1/2 of her money plus $5 on a handbag. She then spent 1/2 of the remaining money plus $3 on a pair of shoes. Finally she spent 2/3 of what was left plus $2 on a skirt. She was then left with $10. How much money did she have at first?
A car travels from Town X to Town Y at a constant speed. If the car increases its speed by 20%, it will reach Town Y one hour earlier. If the car increases its speed by 25% after travelling for 120 km, it will reach Town Y 48 minutes earlier. Find the distance between Town X and Town Y.
A car travels from Town X to Town Y at a constant speed. If the car increases its speed by 20%, it will reach Town Y one hour earlier. If the car increases its speed by 25% after travelling for 120 km, it will reach Town Y 48 minutes earlier. Find the distance between Town X and Town Y.
Solution:
Initial Speed : Increased speed
10 : 12
Time (initiate) : Time (new)
12 : 10
Difference in Time = 1 hr
2 units -----> 1 hr
12 units -----> 12/2 = 6 hr
Initial Speed : Increased speed
4 : 5
Time (initiate): Time (new)
5 : 4
1 unit -----> 4/5 hr
5 units -----> 4 hrs
4 hrs -----> 120 km
6 hrs -----> 180 km
Mrs Tan had a sum of money to spend. She spent 1/2 of her money plus $5 on a handbag. She then spent 1/2 of the remaining money plus $3 on a pair of shoes. Finally she spent 2/3 of what was left plus $2 on a skirt. She was then left with $10. How much money did she have at first?
Students will understand my working with an aid of the Model Drawing...
Solution:
1 unit -----> $12 ($10 + $2)
3 units -----> 12 x 3 = $36
1 unit -----> $39 ( $36 + $3)
2 units -----> 39 x 2 = $78
1 unit -----> $83 ($78 + $5)
2 units -----> $83 x 2 = $166
Amended...
A car travels from Town X to Town Y at a constant speed. If the car increases its speed by 20%, it will reach Town Y one hour earlier. If the car increases its speed by 25% after travelling for 120 km, it will reach Town Y 48 minutes earlier. Find the distance between Town X and Town Y.
Solution:
Initial Speed : Increased speed
10 : 12
Time (initiate) : Time (new)
12 : 10
Difference in Time = 1 hr
2 units -----> 1 hr
12 units -----> 12/2 = 6 hr
Initial Speed : Increased speed
4 : 5
Time (initiate): Time (new)
5 : 4
1 unit -----> 4/5 hr
5 units -----> 4 hrs
6 - 4 = 2 hr
2 hrs -----> 120 km
6 hrs -----> 360 km
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