Ace Drama Company sold some tickets for a children's performance. It sold the same number of $8 and $5 tickets in Week 1 and collected a total of $1664. In Week 2, it sold 96 $8 and $5 tickets. If the company collected $632 more from the sale of $8 tickets than the $5 tickets in the two weeks, how many $8 tickets were sold altogether?
Solution
Week 1
$8 tickets --> 8 units
$5 tickets --> 5 units
Total 13 units --> $1664
1 unit --> $1664 divided by 13 = $128
Value of tickets sold in Week 1
$8 tickets --> 8 x $128 = $1024
$5 tickets --> 5 x $128 = $640
Difference between $8 tickets and $5 tickets in Week 1
$1024 - $640 = $384
Difference between $8 tickets and $5 tickets in Week 2
$632 - $384 = $248
If 96 tickets in Week 2 were equally sold between $5 tickets and $8 tickets, there will be 48 tickets each.
$5 tickets --> 48 x $5 = $240
$8 tickets --> 48 x $8 = $384
Difference between $8 tickets and $5 tickets in Week 2 if equal number of $5 tickets and $8 sold, would be
$384 - $240 = $144
But the difference is $248 and not $144. Instead, we have,
$248 - $144 = $104 (more)
For every $8 sold instead of $5, there would be an increase of ($8 + $5) = $13
$104 (more) divided by $13 = 8 (tickets more)
48 tickets + 8 tickets (more) = 56 $8 tickets sold on 2nd day.
1st Week --> $1024 divided by $8 = 128 (tickets)
Total number of $8 tickets
--> 128 + 56 = 184
Answer: 184 $8-tickets
Sunday, February 21, 2010
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q18
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
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q16
The ratio of the number of boys to the number of girls in School A is 4:1. the ratio of the number of boys to the number of girls in School B is 2:3. School A had twice as many pupils as School B.
a) What is the ratio of boys in School A to the number of girls in School B?
Solution
* School A is multiplied by 2 to give a total of 10 units. This is because School B has 5 units. School A has twice the number of pupils as School B.
(a)
Boys from School A --> 8 units
Girls from School B --> 3 units
Ratio of number of boys in School A to number of girls in School B
--> 8 : 3
Answer: 8 : 3
b)
School B
* Before is multiplied by 5 and After is multiplied by 2 to make the boys have a common unit of 10 for both Before and After, because there was no transfer of boys.
Girls increased by 1 unit after the transfer
1 unit--> 30
Number of girls in School B after transfer
16 units --> 16 x 30 = 480
Answer: 480 girls
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q15
Three men, A, B and C, worked together to paint a wall. If the painting was done by one man, the time taken to complete the wall for A, B and C would have been 6 hours, 8 hours and 12 hours respectively. A and B had painted for 3 hours after which A rested. B and C then continued with the painting. What would be the total number of hours taken to complete the wall? (Give your answer as a mixed number.)
Solution
First 3 hours
A painted for 3 h --> 3/6 = 1/2 (of the wall)*
B painted for 3 h --> 3/8 = 3/8 (of the wall)**
1/2 + 3/8 = 7/8 (of the wall was painted in first 3 hours)
* A takes 6h to paint the whole wall, therefore, in 3h, 3/6
** B takes 8h to paint the whole wall, therefore, in 3h, 3/8
A rests, B and C continue to paint remaining 1/8 of wall
Ratio of hours taken to paint whole wall
B : C
8 : 12
2 : 3
B takes less time than C, therefore B would have painted more of the wall
Ratio of amount of wall painted
B : C
3 : 2 --> Total units is 5
Time taken for B to paint whole wall
5/5 of wall --> 8h
Therefore, 3/5 of wall --> (3/5) x 8h = (24/5)h
Since only 1/8 of wall remains
1/8 of wall left --> (1/8) x (24/5)h = 3/5 h
Total time taken
--> 3h + 3/5 h = 3 and 3/5 hours
Answer: 3 and 3/5 hours
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q14
Mr Lim paid $134.40 for some jackfruits and pomeloes. The cost of the pomelo was 0.8 that of a jackfruit. A pomelo cost $5.60. If all the pomeloes cost $22.40 more than the jackfruits, how many fruits did he buy?
Solution
2 units --> $134.40 - $22.40 = $112
1 unit --> $112 divided by 2 = $56
Cost of Pomeloes
--> $56 + $22.40 = $78.40
Number of Pomeloes bought
--> $78.40 divided $5.60 (per pomelo)
= 14 pomeloes
Cost of of 1 pomelo is 0.8 of 1 jackfruit
Pomelo --> 8 units
Jackfruit--> 10 units
(Pomelo) 8 units --> $5.60
1 unit --> $5.60 divided by 8 = $0.70
(Jackfruit) 10 units --> 10 x $0.70 = $7
Number of Jackfruits bought
--> Total cost - cost of pomeloes
$134.40 - $78.40 = $56
$56 divided by $7 (per jackfruit) = 8 (jackfruits)
Total number of fruits
14 (pomeloes) + 8 (jackfruits) = 22 fruits
Answer: 22 fruits
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q13
The ratio of Jane's allowance to Olivia's allowance was 4:3. After Jane and Olivia were given $15 and $8 respectively, the ratio of Jane's allowance to Olivia's allowance became 3:2. How much allowance did Jane have at first?
Solution
Jane
4 units (at first) + $15 (given) --> 3 parts
Olivia
3 units (at first) + $8 --> 2 parts
2 parts --> 3 units + $8
1 part --> 3/2 units + $4
3 parts --> 3 x 3/2 units + 3 x $4
= 9/2 units + $12
(Jane) 3 parts --> 4 units + $15
(Olivia) 3 parts --> 9/2 units + $12
(Olivia) 9/2 units + $12 --> (Jane) 4 units + $15
9/2 units + $12 --> 8/2 units + $15
9/2 units - 8/2 units --> $15 - $12
1/2 unit --> $3
1 unit --> $6
Jane at first
4 units --> 4 x $6 = $24
Answer: $24
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 Q10
In the figure shown below, SUVX is a square. STU is an equilateral triangle and TXW is a straight line.
a) Find the value of Angle STX.
b) Find the value of Angle WVX.
Solution
a)
Line TZ passes through V, while line TY is passes through the centre of Line SU.
Angle STX is 1/4 of Angle STU.
Angle STU is 60 degrees (Triangle STU is equilateral)
Angle STX --> (1/4) x 60 degrees = 15 degrees
Answer: 15 degrees
b)
Angle SXT = 15 degrees (Triangle STX is isosceles)
Angle TXV --> (90 - 15) degrees = 75 degrees
Angle WXV --> (180 - 75) degrees = 105 degrees
Angle WVX
--> (180 - 105) degrees divided by 2 = 37.5 degrees
(Triangle WVX is isosceles)
Answer: 37.5 degrees
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q9
Nigel had a total of 227 durians and pears. He sold half of the durians and bought another 40 pears. As a result, he had an equal number of durians and pears.
a) How many durians were there at first?
b) How many pears were there at first?
Solution
(a)
3 units --> 267
1 unit --> 267 divided by 3 = 89
(Durians) 2 units --> 2 x 89 = 178
Answer: 178 durians
(b)
(Pears) 1 unit - 40
--> 89 - 40 = 49
Answer: 49 pears
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
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q6
(a) Arif is 2x years old. His father is 4 times as old as he. His mother is 3 years younger than his father. What is their total age in terms of x?
(b) If x is = 4, find their total age.
Solution
(a)
Arif --> 2x
Father --> 4 x 2x = 8x
Mother --> 8x - 3
Total --> 2x + 8x + 8x - 3 = 18x - 3
Answer: (18x - 3) years
(b)
18(4) - 3
= 72 - 3
= 69
Answer: 69 years
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q5
A container with Bottle A placed in it has a mass of 4.27 kg. An identical container with Bottle B placed in it has a mass of 6.58 kg. The mass of Bottle A is 1/3 that of Bottle B. What is the mass of the Bottle A? Give your answer correct to 2 decimal places.
Solution
Bottle A --> 1 unit
Bottle B --> 3 unit
Container + Bottle A (1 unit) --> 4.27 kg
Container + Bottle B (3 units) --> 6.58 kg
3 units - 1 unit --> 6.58 kg - 4.27 kg
2 units --> 2.31 kg
1 unit --> 2.31 kg divided by 2 units = 1.155 kg
1.155 kg --> 1.16 kg correct to 2 decimal places
Answer: 1.16 kg
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q4
Box A contains only one-dollar coins. Box B contains only fifty-cent coins and Box C contains only twenty-cent coins. Box A has 5 times as many coins as Box C. Box B contains 12 coins fewer than Box A. Box C contains half the number of coins in Box B. How much money is there in Box B?
Solution
2 units --> 5 units - 12
3 units --> 12
1 unit --> 12 divided by 3 = 4
(Box B)
5 units - 12
-->(5 x 4) - 12
= 20 - 12
= 8 (coins)
8 coins x $0.50 = $4
Answer: $4
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q3
The ratio of the number of Chloe's stickers to the number of Faith's stickers is 3:5. The ratio of the number of Faith's stickers to Melissa's stickers is 6:7. If Melissa has 204 stickers more than Chloe, how many stickers do they have altogether?
Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q1
LMNO is a square. PQN and PLQ are isosceles triangles. Angle QNM is 23 degrees. Find Angle NPQ.
Wednesday, February 10, 2010
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q18
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q17
From the table above
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q16
The number of pupils in Team A to the number of pupils in Team B is in the ratio of 7:6. If 45 pupils are transferred from Team A to Team B, the ratio will become 2:3. How many pupils are there altogether? Team A had a decrease of
Tuesday, February 09, 2010
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q15
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q14
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q13
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?
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q11
James spends 20% of his monthly income on transport, 30% of it on food and 10% of the remainder on clothes. He saves the rest of his income. If his monthly savings is $900, find his monthly income.
Solution
(Saves)
90% of 50% --> $900
(90/100) x (50/100) x 100% --> $900
45% --> $900
1%--> $900 divided by 45 = $20
(Monthly Income)
100% --> 100 x $20 = $2000
Answer: $2000
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q10
What is the perimeter of Pattern 10?
Friday, February 05, 2010
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q9
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q8
The rectangle ACEG is divided into 4 parts. BCEF is a square. Each part has a different area. Find the area X.
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q7
The table below shows the rates for water consumption.
Thursday, February 04, 2010
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q6
Ai Tong Sch 2009 P6 CA1 Math Paper 2 Q5
Solution
Shaded part --> 1 unit
Area of Square A --> 5 units (shaded area is 1/5 of Area of Square A)
Note that Square A has 4 units of unshaded and 1 unit of shaded area.
Note that Square B has 19 units of unshaded and 1 unit of shaded area.
Total Area
= 24 units
Fraction of shaded area to area of whole figure
--> 1/24
