Tutor MathsGuru: Ask me for your burning Maths questions!

[amberzbon]

Hi, I need help in these 2 qns


1) Ann spent $5850 on some bags and wallets. She bought 5 times as many bags as wallets. She paid $4400 more for bags than wallets. Each bag cost $60 more than a wallet. Find the cost of one wallet.

2)Eileen gets $2 more allowance than Mabel each week. Each girl spends $21 per week and saves the rest. When Eileen saves $72, Mabel only saves $48. How much allowance does Mabel get each week?

Thanks in advance

[mathsguru]

amberzbon:

Hi, I need help in these 2 qns


1) Ann spent $5850 on some bags and wallets. She bought 5 times as many bags as wallets. She paid $4400 more for bags than wallets. Each bag cost $60 more than a wallet. Find the cost of one wallet.

2)Eileen gets $2 more allowance than Mabel each week. Each girl spends $21 per week and saves the rest. When Eileen saves $72, Mabel only saves $48. How much allowance does Mabel get each week?

Thanks in advance

Hi Amberzbon,

Here're my solutions. Hope they are clear enough!

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=TsJQ5SS

http://www.postimage.org/image.php?v=TsJQ8n0

[YLH88]

Hi Mathsguru,


Need your help with the following questions :

1) In the figure below, which is not drawn to scale, 1/5 of the circle is shaded. The ratio of the area of the square to the sum of area of the rectangle and the circle is 1 : 2. 60% of the square is shaded. 1/3 of the rectangle is shaded. What is the ratio of the area of the circle to the square to the rectangle ?
(ans : 5 : 10 : 15)

http://www.postimage.org/image.php?v=TsM_an9


2) SCGS SA1 2009 P2 Qn 17
A set of dictionaries which fitted exactly 4 shelves, each 2.05 m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of dictionaries between the two sets ?
(ans : 120)


3) Red Swastika SA1 2009 P2 Qn 16
Alan, Ben and Charles had 864 trading cards. Ben won some of the cards from Alan and as a result, Ben's cards increased by 50%. Charles then won some cards from Ben and Charles' cards increased by 40%. Finally, Charles lost some of his cards to Alan and Alan's cards increased by 20%. How many cards did Alan have at first ?
(ans : 368)


4) Red Swastika SA1 2009 P2 Qn 17
The distance between Town P and Town Q was 480 km. At 10 30, Mr Poh left Town P travelling at a constant speed towards Town Q to meet his wife. At the same time, Mrs Poh who was at Town Q travelled towards Town P at a constant speed. Mr and Mrs Poh met each other at 14 30. Mrs Poh was travelling at 20 km/h faster than Mr Poh. What was the speed Mrs Poh was travelling at ?
(ans : 70 km/h)


5) Red Swastika SA1 2009 P2 Qn 9
Mr Fernandex drove from home to work at 60 km/h. After work, he needed to rush home for dinner and increased his speed on his way home by 30 km/h. As a result, he took 5 minutes less than what he had taken on his way to work. What was the distance between his house and office ?
(ans : 15 km)


If the same set of questions have been posted before, would greatly appreciate if someone can point me to the pages.

Thank you very much!

[Vanilla Cake]

YLH88:

1) In the figure below, which is not drawn to scale, 1/5 of the circle is shaded. The ratio of the area of the square to the sum of area of the rectangle and the circle is 1 : 2. 60% of the square is shaded. 1/3 of the rectangle is shaded. What is the ratio of the area of the circle to the square to the rectangle ?


http://www.postimage.org/image.php?v=TsM_an9

Area of square : Area of rectangle+Area of circle
1 : 2
10 : 20

Shaded area of square = 60% = 3/5 = 3/5x10units = 6 units
1/3R+1/5C = 6 units
(R=Rectangle and C = Circle)
Multiply by 3
R+3/5C = 18 units - (1)

R+C = 20 units - (2)

(2)-(1)
2/5C = 2 units
C = 5/2x2 = 5 units
R=20units-5units = 15 units

C:S:R
5:10:15
1:2:3

Ratio of the area of the circle to the square to the rectangle = 1:2:3

[Vanilla Cake]

YLH88:

2) SCGS SA1 2009 P2 Qn 17

A set of dictionaries which fitted exactly 4 shelves, each 2.05 m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of dictionaries between the two sets ?

Length of 4 shelves = 4x2.05 m = 8.2 m = 820 cm
Number of new dictionaries = 820÷5 = 164
Number of old dictionaries = (164÷4)x7 = 287
Difference in the number of dictionaries between the two sets = 287-164 = 123

YLH88:

3) Red Swastika SA1 2009 P2 Qn 16
Alan, Ben and Charles had 864 trading cards. Ben won some of the cards from Alan and as a result, Ben's cards increased by 50%. Charles then won some cards from Ben and Charles' cards increased by 40%. Finally, Charles lost some of his cards to Alan and Alan's cards increased by 20%. In the end, they realised that they each had an equal number of cards.How many cards did Alan have at first ?

Hi YLH88,
You missed out and didn't type this important statement highlighted in red colour in the question.

In the end
A = 288
B = 288
C = 288

Note: 864/3 = 288

120%=288
100%=240
20%=48

A = 240
B = 288
C = 336

140% = 336
100% = 240
40% = 96

A = 240
B = 384
C = 240

150% = 384
100% = 256
50% = 128

A = 368
B = 256
C = 240

At first, Alan had 368 cards

[Vanilla Cake]

YLH88:

4) Red Swastika SA1 2009 P2 Qn 17

The distance between Town P and Town Q was 480 km. At 10 30, Mr Poh left Town P travelling at a constant speed towards Town Q to meet his wife. At the same time, Mrs Poh who was at Town Q travelled towards Town P at a constant speed. Mr and Mrs Poh met each other at 14 30. Mrs Poh was travelling at 20 km/h faster than Mr Poh. What was the speed Mrs Poh was travelling at ?

20 x 4 = 80 km
(480-80)÷2 = 200 km

Distance travelled by Mr Poh = 200 km
Distrance travelled by Mrs Poh = 280 km

Speed at which Mrs Poh was travelling = 280÷4 = 70 km/h

YLH88:

5) Red Swastika SA1 2009 P2 Qn 9
Mr Fernandex drove from home to work at 60 km/h. After work, he needed to rush home for dinner and increased his speed on his way home by 30 km/h. As a result, he took 5 minutes less than what he had taken on his way to work. What was the distance between his house and office ?

Ratio of speed = 90 : 60 = 3 : 2
Ratio of time = 60 : 90 = 2 : 3

Time taken @ 90 km/h = 2 units
Time taken @ 60 km/h = 3 units
Difference in time taken = 5/60 = 1/12 hour = 1 unit

Distance travelled = 2 units x 90 km/h = 2x1/12x90 = 15 km
Distance between his house and office was 15 km

Mathsguru had posted her solution for this Fernandez's speed question recently. Pls wait for her to repost her solution again or you have to browse through this thread.
Thanks.

YLH88:

If the same set of questions have been posted before, would greatly appreciate if someone can point me to the pages.

Sorry, can't help due to the numerous pages in this thread and I have to study for my CT.
:imsorry:

[Herbie]

HI, Thanks MathsGURU


Can help with the qn below:

Belinda has 200 more books than Alan, Belinda gives 60% of her books to Alan. Alan then gives 25% of her books back to Belinda. In the end, Alan has 200 more books than Belinda. How many books does Belinda have at first?

Thanks!

[Vanilla Cake]

Herbie:

HI, Thanks MathsGURU


Can help with the qn below:

Belinda has 200 more books than Alan, Belinda gives 60% of her books to Alan. Alan then gives 25% of her books back to Belinda. In the end, Alan has 200 more books than Belinda. How many books does Belinda have at first?

Thanks!

Hi Herbie,
Your question is similar to this http://www.postimage.org/image.php?v=gxK_oj0 on Sat May 01, 2010 8:15 pm. Only the names are changed in your question but the concept applied to solve the question is the same.

Hope this helps while waiting for Mathsguru to repost her solution.

[YLH88]

Hi Vanilla Cake,


Sorry for the missing sentence in Qn 3 :oops:

Thank you so much for all the solutions !! All the best to your exam tomorrow.

[Dharma]

Herbie:

HI, Thanks MathsGURU


Can help with the qn below:

Belinda has 200 more books than Alan, Belinda gives 60% of her books to Alan. Alan then gives 25% of her books back to Belinda. In the end, Alan has 200 more books than Belinda. How many books does Belinda have at first?

Thanks!

Belinda gives 60% of her books to Alan
Belinda : 100u – 60u = 40u
Alan : 100u – 200 + 60u = 160u – 200

Alan gives 25% of his books to Belinda
Belinda : 40u + (40u – 50) = 80u - 50
Alan : 160u – 200 – (40u – 50) = 120u – 150

120u – 150 – (80u – 50) = 200
40u – 100 = 200
40u = 300
1u = 7.5

No. of books Belinda had at first = 100u = 750