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 Forum Index >  Test Paper Related >  Primary 6 Matters
 P6 Maths! 2012 Red Swastika Paper 2 Q11, Q13 & Q16
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By: geniuskids (offline)  Sunday, May 12 2013 @ 08:24 PM CDT (Read 1086 times)  
geniuskids

Hi there, pls help!

Q11 : Mrs Tan had enough money to buy 5 cupcakes or 7 curry puffs. If each cupcake cost $0.50 more than each curry puff, how much money did Mrs Tan have?



Q13 : Anne, Beth, Calia and Debby went for a meal together. Anne paid $180. Beth paid $80 less than Calia. Calia paid 3/10 of the total bill while Debby paid 1/5 of the total bill. How much did Beth pay for the meal?



Q16: Ranice had some red and blue balloons to sell at a fun fair. The number of red balloons was 25% of the total number of balloons. After selling 30 red balloons and 30 blue balloons, the number of red balloons was 25% the number of blue balloons.

(a) How many balloons did she have at first?
(b) If each balloon cost $2.50, how much did she collect from selling the balloons.

Many Thanks!

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By: jo sarah (offline)  Sunday, May 12 2013 @ 11:08 PM CDT  
jo sarah

Q11 : Mrs Tan had enough money to buy 5 cupcakes or 7 curry puffs. If each cupcake cost $0.50 more than each curry puff, how much money did Mrs Tan have?

Solution, Q11:
Since 5 cupcakes (C) cost as much as 7 puffs (P), then
..............----------------------------------------------
5 C........|.......................................................|
.............-----------------------------------------------
7 P........|.......................................................|
.............-----------------------------------------------

so, we divide the 2 long boxes into 35 (=7 x 5) equal units (u).
That makes cost of 1 C = 7 u,
and cost of 1 P = 5 u
each C costs $0.50 more than each P, therefore, 2 u ---> $0.50
that is to say, 1 u ---> $0.25

So, Mrs Tan had 35 x $0.25 = $8.75. Big Grin


Q13 : Anne, Beth, Calia and Debby went for a meal together. Anne paid $180. Beth paid $80 less than Calia. Calia paid 3/10 of the total bill while Debby paid 1/5 of the total bill. How much did Beth pay for the meal?

Solution, Q13:
Note the question speaks of C and D paying some fraction of the total bill.
So these two together paid 3/10 + 1/ 5 =1/2 of total bill.
That is, A and B together paid 1/2 of total bill too.
If the total bill is 10 units (u), then
.................A...........B............C..........D
paid:.....$180....3u - $80......3u.........2u

You work from: $180 + 3u - $80 ---> 5u
so that, ........................2u ---> $100
And, B paid: 3u - $80 = $50 x 3 - $80 = $70 Big Grin


Q16: Ranice had some red and blue balloons to sell at a fun fair. The number of red balloons was 25% of the total number of balloons. After selling 30 red balloons and 30 blue balloons, the number of red balloons was 25% the number of blue balloons.

(a) How many balloons did she have at first?
(b) If each balloon cost $2.50, how much did she collect from selling the balloons.

Solution, Q16:
convert percentages to frations... easier to handle Laughing Out Loud

So, in the beginning:
.......--------------
R....|................|.........................................1 unit (u)
......-------------------------------------------
B....|................|................|................|........3 u
......-------------------------------------------

After selling equal no. of 30 of each type, we change 1 u to 1 part (p) + 30, so that:
.......--------------
R....|.30.|.........|.........................................1 p + 30
......-------------------------------------------
B....|.30 |.........|.30 |.........|.30 |.........|........3 p + 30 + 60
......-------------------------------------------

So, now, taking away 30 from R and B,
R: 1 p
B: 3 p + 60 = 4 p [because R is 1/4 (25%) B]

That is to say, 1 p ---> 60 balloons
and, 1 u ---> 60 + 30 = 90
So she had 4 x 90 = 360 balloons at first. Big Grin

and, part (b) is simple. She collected $2.50 x 360 = $900 Big Grin

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By: echeewh (offline)  Sunday, May 12 2013 @ 11:31 PM CDT  
echeewh

Hey Geniuskids,

Following pls find my worked solution:

Q11

<Cost model>
1CC |------|<50>|
1CP |------|

If 1CP = 1u , then ...

5CC = 5u + 250

Given that total money is enough to buy 5CC or 7CP, we have ...

5u + 250 = 7u
7u - 5u --> 250
2u --> 250
1u --> 125

Total money = 7u
7u --> 7 × 125 = 875 = $8.75

=======

Q13

Total Bill = 10u
C: (3/10)total = 3u
D: (1/5)total = (2/10)total = 2u
A: $180
B: C - 80 = 3u - 80
C + D = 3u + 2u = 5u = (1/2) total bill
So, A + B = (1/2) total bill = C + D

A + B = C + D
180 + 3u - 80 = 5u
5u - 3u = 100
2u --> 100
1u --> 50

B = 3u - 80
3u - 80 --> (3 × 50) - 80 = 150 - 80 = $70

=======

Q16

*** - for alignment purpose

Apply <Unchanged Difference> concept to this problem sum, i.e. difference in number of R, B balloons at first is the same in the end.

<Before>
R: (1/4) total
B: (3/4) total

R : B * Diff
1 : 3 ** 2 -- (1)

<Process>
R: 30 sold
B: 30 sold

<After>
R : B * Diff
1 : 4 ** 3 -- (2)

To make Diff<before> and Diff<after> the same, multiply (1) 3x, (2) 2x.

<Before>
R : B * Diff
3 : 9 ** 6 -- (3)

<After>
R : B * Diff
2 : 8 ** 6 -- (4)

Note theres a decrease of 1u from both R, B in the ratios. Hence,

1u --> 30

(a)
Total balloons (at first) = 12u --> 12 × 30 = 360

(b)
60 balloons were sold.

60 × 250 = 15000 = $150.00

=========

Trust this helps.

Do let me know again if this is different from your Answerkey or if theres further clarification.

< Note for Geniuskids:
You quoted "... You have been a great help in my journey without P6 Maths tuition in this era..."
These 3 Questions, i believe, are from the 4-marks category in Paper 2, and if you are not able to do these, then I feel you need more practices and refine your skills, and in fact, perhaps , consider taking me on as your Coach as well. Idea Big Grin >


Cheers,
Edward

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