
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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Registered: 11/12/11 Posts: 169





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

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Registered: 03/20/12 Posts: 111





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 4marks 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. >
Cheers,
Edward

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Registered: 04/21/11 Posts: 623



