At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference?
Solution
Male ----- 120%
Female ----- 100%
Speakers
Male : Female
8 (parts) : 5 (parts)
Participants
Male : Female
1 (unit) : 1 (unit)
Men ----- 8 parts + 1 unit
Women ----- 5 parts + 1 unit
But since there are 20% more women than men,
Women ----- 5 parts x 120% + 1 unit x 120%
= 6 parts + 1.2 units
Men ----- Women
8 parts + 1 unit ----- 6 parts + 1.2 units
8 parts - 6 parts ----- 1.2 units - 1 unit
2 parts ----- 0.2 unit
1 part ----- 0.1 unit
10 parts ----- 1 unit
or
1 unit ----- 10 parts
(a)
Male Speakers ----- 8 parts
Male Participants ----- 1 unit or 10 parts
Male Speakers : Male Participants
8 : 10
4 : 5
Answer: 4 : 5
(b)
Speakers
Male : Female
8 (parts) : 5 (parts) -- (altogether 13 parts)
Participants
Male : Female
1 (unit) : 1 (unit)
10 (parts) : 10 (parts) -- (before)
- 40 : + 60 -- (40 males left; 60 females joined)
3 (units) : 4 (units) -- (3/4 as many male as females in the end)
(Male) 3 units ----- 10 parts - 40
(Female) 4 units ----- 10 parts + 60
(Female) - (Male)
4 units - 3 units ----- 10 parts + 60 - 10 parts - (-40)
1 unit ----- 60 + 40
1 unit ----- 100
(Male after)
3 units ---- 3 x 100 = 300
(Male before)
10 parts ---- 300 + 40 (need to add the 40 who left)
10 parts ----- 340
1 part ---- 34
All speakers
13 parts ---- 13 x 34 = 442
Answer: 442 speakers
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Wednesday, September 14, 2011
Catholic High School 2010 PSLE Math Prelim Paper 2 Q18
Sunday, April 24, 2011
ACS Primary 2010 SA1 Math Paper 2 Q16
Mr Wu had some badges and decided to give them to his two sons, Sean and Matthew. Mr Wu gave 1/3 of the badges and 8 more badges to Sean. He then gave 3/4 of the remainder to Matthew but took back 2 badges. Mr Wu was left with 26 badges. How many badges did Mr Wu have at first?
Solution
Assume all badges --> 1 unit
Mr Wu was left with,
----- 1/4 of Remainder + 2
----- 1/4 x (2/3 unit - 8) + 2
= (1/6 unit - 2) + 2
= 1/6 unit - 2 + 2
= 1/6 unit
1/6 unit --> 26 badges
1 unit ----- 26 divided by 1/6
= 26 x 6
= 156
Answer: 156 badges
Wednesday, April 13, 2011
ACS Primary 2010 SA1 Math Paper 2 Q12
Weiming had 2/3 as many stickers as Shiyang. After Weiming gave 52 stickers to Shiyang, Weiming had 2/5 as many stickers as Shiyang. How many stickers did Weiming have at first?
Solution
*(x7) and (x5) to give a common total of 35 units for both "At first" and "In the end", since there is no change in the total number of stickers.
Weiming gave
14 units - 10 units ---- 52
4 units ----- 52
1 unit ----- 52 divided by 4 = 13
Weiming at first
14 units x 13 = 182
Answer: 182 stickers
Saturday, March 19, 2011
Another Math Problem Sum
I received another request through email from a reader. Anyone willing to help her out?
==========
Alice, Barbie,Cora and Daylia are given some stickers. The number of stickers Alice has is 25% of the number of stickers the other 3 children have. The number of stickers Barbie has is a third of the number of stickers the other children have, while Cora has half of the number of stickers the other children have. If Daylia has 78 stickers, how many stickers does each of the other children have?
Thank You for taking your time to read this. I appreciate it if you could give me a solution to this problem as soon as possible.
==========
Sunday, August 22, 2010
RGS Primary 2009 PSLE Math Prelim Paper 2 Q18
Solution
(K) 20 units --> 10 parts + 1625
1 unit --> 1785 divided by 14 = 127.5
(a)
(b)
Lily in the end
--> 3 units + 80
(3 x 127.5) + 80
= 382.5 + 80
= 462.5
Answer: $462.50
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Thursday, August 19, 2010
RGS Primary 2009 PSLE Math Prelim Paper 2 Q4
Find the number that is exactly between 4/5 and 1 and 1/3.
Solution
4/5 + 1 and 1/3
= 12/15 + 1 and 5/15
= 2 and 2/15
2 and 2/15 divided
= 1 and 1/15
Answer: 1 and 1/15
Tuesday, July 20, 2010
ACS Primary 2009 PSLE Math PrelimPaper 2 Q15
There were 192 apples and pears in a box. John removed 2/5 of the apples from the box and he added 24 pears into the box. As a result, there was an equal number of apples and pears left in the box. How many more apples than pears were there in the box at first?
Solution
3 units --> 1 part + 24
5 units + 1 part --> 192
3 units - 1 part --> 24
(5 units + 3 units) + (1 part - 1part) --> 192 + 24
8 units --> 216
1 unit --> 216 divided by 8 = 27
At first
(Apples) 5 units --> 5 x 27 = 135
(Pears) 192 - 135 = 57
Apples more than pears
--> 135 - 57 = 78
Answer: 78 more apples
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Sunday, July 18, 2010
ACS Primary 2009 PSLE Math Prelim Paper 2 Q9
The pie chart below shows the different types of muffins sold in a bakery. A total of 240 muffins were sold.
a) How many banana muffins were sold?
b) If a chocolate muffin cost $1.60, how much did the bakery collect from the sale of chocolate muffins?
Solution
a) (1/4) x 240 = 60
Answer: 60 banana muffins
b)
Cheese --> (1/8) x 240 = 30
Blueberry --> (20/100) x 240 = 48
Banana --> 60
Chocolate Chip --> 68
Total for the above
--> 30 + 48 + 60 + 68 = 206
Chocolate --> 240 - 206 = 34
Sale collected from chocolate muffin
--> 34 x $1.60 = $54.40
Answer: $54.40
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ACS Primary 2009 PSLE Math Prelim Paper 2 Q2
Box X contains 6 times as many oranges as Box Y. Box Z contains 111 fewer oranges than Box X. If Box Y contains 1/3 the number of oranges in Box Z, find the total number of oranges in the 3 boxes.
Solution
X --> 6 units
Answer: 370 oranges
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Wednesday, April 14, 2010
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q18
Sparkles Jewellery Shop sold diamonds, rubies and emeralds. 3/5 of the gemstones were diamonds. There were 168 fewer rubies than diamonds. The ratio of the number of rubies to the number of emeralds was 7:3. After some rubies were sold, 30% of the remaining gemstones in the shop were rubies and emeralds.
a) How many rubies were sold?
b) Find the percentage decrease in the number of gemstones. Leave your answer as a fraction.
Solution
Rubies --> 7/10 of 2/5 = 14/50
Diamonds - Rubies --> 168 (more diamonds than rubies)
3/5 - 14/50 = 168
16/50 --> 168
1/50 --> 168 divided by 16 = 10.5
Rubies + Emeralds (2/5 of whole)
20/50 --> 20 x 10.5 = 210
2/5 of whole --> 210
1/5 of whole --> 210 divided by 2 = 105
(Diamonds) 3/5 of whole --> 3 x 105 = 315
After selling, Rubies and Emeralds make up 30%, while Diamonds make up 70%.
Diamonds 70% --> 315
10% --> 315 divided by 7 = 45
Rubies and Emeralds 30% --> 3 x 45 = 135
(a)
(Rubies and Emeralds before selling) - (Rubies and Emeralds after selling)
--> 210 - 135 = 75
Answer: 75 rubies
(b)
Percentage decrease in number of gemstones
1/50 of gemstones --> 10.5
50/50 of gemstones -> 50 x 10.5 = 525
75 rubies sold
--> (75/525) x 100% = 14 and 2/7 %
Answer: 14 and two-sevenths %
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q16
Ali and Minhua were playing a card game using 96 cards. In the first game, Minghua lost 1/5 of his cards to Ali. In the second game, Ali lost 1/3 of his cards to Minghua. After the second game, both boys had the same number of cards. How many cards did Ali have at first?
Solution
Before 1st game
Minghua --> 5 units
Ali --> 11 units
Total 16 units --> 96
1 unit --> 96 divided by 16 = 6
11 units --> 66
Answer: 66 cards
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q13
Abbie, Ellen and Faheem sold umbrellas to raise funds for charity. Each umberlla was priced at $22.50. Abbie sold 1/6 of the umbrellas while Ellen and Faheem sold the remaining umbrellas in the ratio of 2:7 respectively. If Faheem sold 364 umbrellas more than Abbie, what was the total amount of money collected by them?
Solution
Abbie --> 1/6
Remaining --> 5/6
Since ratio for Ellen : Faheem is 2 : 7,
Faheem sold 7/9 of remainder
Faheem (7/9 of the remaning 5/6)
--> 7/9 x 5/6 = 35/54
(Faheem - Abbie) --> 35/54 - 1/6 = 13/27
13/27 --> 364 (Faheem sold 364 more than Abbie)
1/27 --> 364 divided by 13 = 28
27/27 --> 27 x 28 = 756
756 x $22.50 = $17 010
Answer: $17 010
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q11
Jai, Maira and Lynn have 760 stickers altogether. Jai has 8/9 as many stickers as Maira and 6/11 as many stickers as Lynn. If Jai and Lynn want to have an equal number of stickers, how many stickers must Lynn give to Jai?
Solution
(48 + 54 + 88) units --> 760 stickers
190 units --> 760
1 unit --> 760 divided by 190 = 4
Lynn must give Jai 20 units for Lynn and Jai to have equal number of stickers.
20 units --> 20 x 4 = 80
Answer: 80 stickers
CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q8
Kumar spent $1729 on a set of encyclopedia. H spent 1/4 of the remainder on a camera and still had 2/5 of his money left. Find the total amount of money he had at first.
Solution
3/5 of money --> $1729 + 1 unit
(multiply above by 3)
9/5 of money --> $5187 + 3 units
2/5 of money --> 3 units
9/5 - 2/5 --> $5187 + 3 units - 3 units
7/5 --> $5187
1/5 --> $5187 divided by 7 = $741
5/5 --> 5 x $751 = $3705
Answer: $3705
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CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q3
Mr Ong had 5 kg or rice. After he sold 5/12 of it, he repacked the remaining rice into smaller packets of 2/3 kg each. How much rice had he left?
Repacked this 35 twelfths kg into packets of 8 twelfths kg (2/3 kg --> 8/12 kg)
35 twelfths divided by 8 packets --> 4 wholes and 3 twelfths
Friday, February 19, 2010
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q17
John had some red and blue marbles in a box. The sum of 1/4 of the red marbles and 2/5 of the blue marbles in the box is 64. The sum of 3/4 of the red marbles and 4/5 of the blue marble in the box is 144.
a) How many red marbles are there in the box?
b) How many blue marbles are there in the box?
Solution
Red (all marbles) --> R R R R
Blue (all marbles) --> B B B B B
1/4 or red marbles and 2/5 or blue marbles -- > 64
R + B B --> 64
3/4 of red marble and 4/5 of blue marbles --> 144
R R R + B B B B --> 144
R + B B --> 64 (multiply all by 2)
R R + B B B B --> 128
We now have
R R R + B B B B --> 144
R R + B B B B --> 128
R --> 144 - 128 = 16
a)
Number of Red Marbles
R R R R --> 4 x 16 = 64
Answer: 64 red marbles
b)
R + B B --> 64
16 + B B --> 64
B B --> 64 - 16 = 48
B --> 48 divided by 2 = 24
Number of Blue Marbles
B B B B B --> 5 x 24 = 120
Answer: 120 blue marbles
Wednesday, February 17, 2010
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q12
Rahim's age is 2/9 of his grandfather's. His grandfather will be 100 years old in 19 years' time. In how many years' time will Rahim's age be 1/4 of his grandfather?
Solution
Now
Rahim --> 2 units
Grandfather --> 9 units
19 years' time (Grandfather)
9 units + 19 --> 100
9 units --> 100 - 19 = 81
1 unit --> 81 divided by 9 = 9
Now
Rahim --> 2 x 9 years = 18 years
Grandfather --> 9 x 9 years = 81 years
Difference between Grandfather and Rahim
--> 81 years - 18 years = 63 years
Future (when Rahim 1/4 of Grandfather's age)
Rahim --> 1 unit
Grandfahter --> 4 units
But Rahim is 63 years younger
4 units - 1 unit --> 63 years
3 units --> 63 years
1 unit --> 63 years divided by 3 = 21 years
Rahim now --> 18 years
Rahim in future --> 21 years
21 years - 18 years = 3 years
Answer: 3 years
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q11
There were some marbles in a box. Sofie took out 2/5 of the marbles and put in 6 more. Then John took out 1/6 of the remaining marbles and put in 5 more. there were 25 marbles left. How many marbles were in the box at first?
Solution
6 units - 1 unit + 6 - 1 + 5 --> 25 (left in box)
5 units + 10 --> 25
5 units --> 25 - 10 = 15
1 unit --> 15 divided by 5 = 3
Marbles at first
--> 10 units x 3
= 30
(At first, there were 10 units and not 5 units because the 5 units have been cut into halves, giving a total of 10 smaller units)
Answer: 30 marbles
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q8
Wilson and Yi Lin had $71 altogether. Yi Lin and Patrick had $105 altogether. Wilsom hand 3/5 of the money that Patrick had. How much money did Yi Lin have?
Solution
Yi Lin + Patrick
? + 5 units --> $105
Yi Lin + Wilson
? + 3 units --> $71
5 units - 3 units --> $105 - $71
2 units --> $34
1 unit --> $34 divided by 2 = $17
Yi Lin + Wilson
? + 3 units --> $71
? + (3 x $17) --> $71
? + $51 --> $71
? --> $71 - $51 = $20
Answer: $20
Tuesday, February 09, 2010
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q12
20 similar pails of water can fill 5/12 of a container. Another 8 similar pails and 105 similar bowls of water are needed to fill the container to its brim. How many such bowls of water are needed to fill the empty container completely?
