Done by : gladwin (:
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Question 1. (Also Known As the Chocolates and Sweets Question)
Jim bought some chocolates and gave half of it to Ken
Ken bought some sweets and gave half of it to Jim
Jim ate 12 sweets and Ken ate 18 chocolates
The ratio of Jim's sweets to chocolates became 1:7
The ratio of Ken's sweets to chocolates became 1:4
How many sweets did Ken buy?
Answer:68
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Question 1
Solution by using algebra:
Let x be the number of sweets bought
Let y be the number of chocolates bought
Jim:
He has x/2 -12 sweets
He has y/2 chocolates
And there are 7 times as many chocolates as there are sweets.
7(x/2-12) : y/2
14(x/2-12) : y
7x - 168 : y
7x -168 = y
Ken:
He has x/2 sweets
He has y/2 -18 chocolates
And there are 4times as many chocolates as there are sweets.
y/2 -18 : 4(x/2)
y/2 - 18 :2x
y-36 : 4x
y=4x +36
Solving simultaneously and eliminating y
Make y the subject of formula for both equations, i.e.
7x - 168 = y
and
4x + 36 = y
So,
7x - 168 = 4x +36
3x = 204
x = 204/3
= 68
Ken bought 68 sweets.
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Question 1
Solution by doing it mentally:
Jim and Ken had the same number of chocolates after Jim gave half to Ken. And they had the same number of sweets after Ken have half to Jim.
Jim had 12 fewer sweets than Ken after he ate 12.
So Ken's 1 unit of sweets = Jim's 1 unit +12.
And so Ken's 1 : 4 = Jim's 1 unit +12sweets : Jim's 4units +48
After Ken ate 18 chocolates, Jim had 18 chocolates than Ken.
Jim has 7 units of chocolates, Ken has 4 units +48.
So 3units = 48+18
=66
1unit = 66/3
=22
Ken had 22 +12 =34sweets after giving half to Jim.
So he bought 34x2=68
Ken bought 68 sweets.
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Question2 (Also Known As the Angle Question)
Given that ABCD is a square.
EG=EF=EH
AB=BC=CD=DA
EF=BC=DA and AB=GH .. Hence, EG=EH=AB=H
EGH is a Equilateral Triangle.
Answer: 150'
--------------------------------
Question2
Solution
Triangle EGH is a Equilateral Triangle.
Thus, one side of its triangle is 180'/3 =60'
Angle GEH = 60'/2 =30'
Triangle EGF is a isosceles. Hence, angle FGE= angle GFE = (180'-30')/2 =75'
Angle GFE = Angle HFE = 75'
Therefore, angle GFH = 75' x 2 = 150'
Angle GFH is 150'
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Question 3 (Also Known As the Renting Computer Question)
6 Friends decided to rentcomputers from 2pm to 4.30pm.
While 4 of them were playing, the other two would watch.
If the cycle continues, and each of them played for equal number of numbers.
How many minutes will each person get to play?
Answer: 100 minutes
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Question 3
Solution
From 2pm to 4.30pm
Time is 2hour 30minutes = 150minutes
4 x 150mins = 600mins
600mins/6people = 100mins
Each person get to play for 100mins.
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Question 4 (Also Known As the Bicycle Race Question)
Mei and Lin were in a bicycle race.
Mei was travelling at a constant speed of 20km/h and they both did not change their speed.
When Lin completed half of the race, Mei was 3.5km ahead.
Mei completed the race at 10.45am.
What time did Lin complete the race?
Answer: 11.06am
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Question 4
Solution
3.5km x 2 =7km
Speed =20km/h
7km= 7/20 X 1
=0.35h
0.35h = 21mins
Time when Lin complete the race= 10.45am +21mins
= 11.06am
Lin complete the race at 11.06am
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Question 5 (Also Known As the Chocolate and Almond Cookies Question)
Sally baked some cookies to sell.
3/4 of them were chocolate cookies and the remaining were almond cookies.
After she sold 5/6 of the chocolate cookies and 210 almond cookies, she had 1/5 of the cookies
left.
How many cookies did she sell?
Answer: 960
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Question5
Solution
Convert the chocolate 3/4 to 30/40
Convert the almond 1/4 to 10/40
7units of almond is 210.
1unit of almond is 210/7 =30
32units of total number of cookies is 30 x 32 =960
She sells 960 cookies.
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Question 6 (Also Known As the Curry Puff Question)
Curry Puff shop sells puffs at $0.80 each.
Buy 3 get the 4th one at half price.
If a customer has $50, how many curry puffs can he buy if he buys as many as he can?
Answer: 71 Curry Puffs
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Question 6
Solution
First 3 Puffs= $0.80 x 3
= $2.40
4th Puff= $0.80/2
= $0.40
Total= $0.40 + $2.40
= $2.80
280/15= 17
17 x 4= 68
68/4= 17
17 x 2.80= $47.60
$50 - 47.60= $2.40
$2.40/$0.80= 3
68 + 3=71
He can buy 71 Curry Puffs
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Question 7 (Also Known As the Balloon's String Question)
String of 2 big balloons is 90cm
String of 5 small balloons is 1.2m
If both strings are of the same length, there would be 105 more small balloons than the big balloons
How many balloons are there altogether?
Answer: 345
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Question 7
Solution
Big:
90cm=2
30cm=2/3
120cm=2/3 x 4
=8/3
=2 2/3
2.6667big = 1.2m
5small = 1.2m
5/2.6667 = 1.8749766
big : small = 1: 1.8749766
1.8749766 - 1 = 0.8749766
105/0.8749766 = 120
1.8749766 + 1 = 2.8749766
Total Number of Balloons = 120 x 2.8749766
= 345
There are 345 balloons altogether
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Question 8 (Also Known As the Rice for Sale Question)
Shop A has 156kg of rice
Shop B has 72kg of rice
Each shop sold an equal amount of rice and after that, the ratio of the amount of rice left in their shop was 4 : 1.
Find out how much rice has been sold.
Answer: 44kg
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Question 8
Solution
Since they sold an equal amount of rice, the original iffeerence remains the same.
The difference is 156kg - 72kg= 84kg.
Then, the ratio difference is 4units - 1unit = 3units.
Now, that 3units is 84kg, shop B now has left 1unit so it has 84kg/3 = 28kg
To find out the amount of rice sold, 72kg - 28kg = 44kg
The amount of rice sold is 44kg
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Question 9 (Also Known As the Chairs in the hall Question)
6/14 of the chairs in the hall are in rows of 13
Half of the chairs in the hall are in rows of 7
There are 112 more chairs in rows of 7. The rest of the chairs are stacked up.
Find out the total numbers of chairs in the Hall.
Answer: 1568
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Question 9
Solution
Most Of the information given is to fool you!!
All it says is...
6/14 chairs re in a group (You don't need to worry what are they in a group of)
1/2 chairs are in another group (1/2 = 7/14)
6/14 + 7/14
=13/14
There are 112 chairs Left..
14units - 13units
=1unit.
1unit = 112
14units= 112 x 14 = 1568
There are a total of 1568 chairs in the hall.
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Hope You Get All Correct For This 9 Questions found in Section C !!!
(: :D
LoL !!
Thursday, October 22, 2009
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