Tutor MathsGuru: Ask me for your burning Maths questions!

[mathsguru]

YLH88:

Hi Mathsguru,


I'm definitely sure your answer is correct But need you to help explain some queries :

For Qn 1 on the books, why do we need to break the 1 big unit into 4 units ? I thought 3 : 1 is referring to the original units where Mrs Yee has 6 units (160%) and Mdm Ling has 5 units (100%) ?

For Qn 2 on the diagram, 160 - shaded area = 3 x (64 - shaded area), multiple by 3 is it because of the unshaded triangle is 300% of the unshaded rectangle ?

Thank you very much !

Hi YLH88,

Pls see below for my explanations. Hope they are clear enough...

1) To answer your question, we need to go back to how we derive the total number of units Tang has in the end. She has 1.5 times her original 6 units. This means that she will have an additional 3 units.

These 3 units has to be split into 3:1 between Yee & Ling, because of the 3rd sentence in the question --- Yee & Ling gave some books to Tang in the ratio of 3:1. To split 3 units into 4 equally, it will be easier to understand by splitting 3 units into the 12 (i.e. LCM of 3 & 4). Therefore, each unit has to be split into 4.


2) Yes! 300% means 3 times as much.

Cheers,
MathsGuru

[YLH88]

Hi Mathsguru,


Oic ... Thank you for the explanation. Now i understand liao

Regards

[firebird]

Dear mathsguru


Good morning

I am totally lost in the following first 2 maths. However, for the 3rd question, I managed to do on guess and check basis. Nevertheless, would be greatful if you could share a systematic method in solving the 3rd question:

1) Miss Wong had just read a novel with 1008 pages. How many digits were used to number the pages from 1 to 1008 in the novel?

2) Mr. Lee left Town M and travelled towards Town N at an average speed of 80 km/h. An hour later Mr. Ong left Town M and travelled towards Town N at an average speed of 100 km/h. Mr. Ong passed Town Q which was halfway between town M and town N 30 minutes earlier than Mr. Lee. If Mr. Ong reached Town N at 10pm, at what time did Mr. Lee leave town M for town N?

3) 100 people were having a health check up. Their average mass was 63kg. Given that the average mass of the women was 60kg and the average weight of the men was 70kg. How many men were there?

Many thanks
firebird

[CoffeeCat]

firebird:

Dear mathsguru


Good morning

I am totally lost in the following first 2 maths. However, for the 3rd question, I managed to do on guess and check basis. Nevertheless, would be greatful if you could share a systematic method in solving the 3rd question:

1) Miss Wong had just read a novel with 1008 pages. How many digits were used to number the pages from 1 to 1008 in the novel?

2) Mr. Lee left Town M and travelled towards Town N at an average speed of 80 km/h. An hour later Mr. Ong left Town M and travelled towards Town N at an average speed of 100 km/h. Mr. Ong passed Town Q which was halfway between town M and town N 30 minutes earlier than Mr. Lee. If Mr. Ong reached Town N at 10pm, at what time did Mr. Lee leave town M for town N?

3) 100 people were having a health check up. Their average mass was 63kg. Given that the average mass of the women was 60kg and the average weight of the men was 70kg. How many men were there?

Many thanks
firebird

For question 1 you are lost because there is no \"straightforward\" approach. You must do systematic listing.
For Page 1-9 , 1*9 digits are used
10-99 2*90 digits are used
...
...

2)For such speed questions, the most efficient method is to use algebra.
By expressing the distance between town M and Q, you can \"capture\" the given information by siolving
(d/80) - (d/100) = 1.5hr

3) this is a typical chicken-duck-leg scenario.
Use the heuristic of making a supposition.
Assume 100 women, total weight 6000 instead of 6300.
Obvious the difference resulted from the loss of extra weight from men.
so number of men = (6300-6000)/10 = 30.

Judging by the nature of the 1st 2 qns, are these taken from some math olympiad training?

[firebird]

Dear coffeecat


Thanks for the help.

All 3 question were from SA2, year 2009, Rulang Primary School, paper 2.

Regards
firebird

[mathsguru]

firebird:

Dear mathsguru


Good morning

I am totally lost in the following first 2 maths. However, for the 3rd question, I managed to do on guess and check basis. Nevertheless, would be greatful if you could share a systematic method in solving the 3rd question:

1) Miss Wong had just read a novel with 1008 pages. How many digits were used to number the pages from 1 to 1008 in the novel?

2) Mr. Lee left Town M and travelled towards Town N at an average speed of 80 km/h. An hour later Mr. Ong left Town M and travelled towards Town N at an average speed of 100 km/h. Mr. Ong passed Town Q which was halfway between town M and town N 30 minutes earlier than Mr. Lee. If Mr. Ong reached Town N at 10pm, at what time did Mr. Lee leave town M for town N?

3) 100 people were having a health check up. Their average mass was 63kg. Given that the average mass of the women was 60kg and the average weight of the men was 70kg. How many men were there?

Many thanks
firebird

Hi Firebird,

Here are my solutions. Hope they help!


MathsGuru

http://www.postimage.org/image.php?v=Ts7N7x0

http://www.postimage.org/image.php?v=gx8EfI0

http://www.postimage.org/image.php?v=gx8EkHi

[YLH88]

Hi Mathsguru,


Need your help with the below question.

Yusof had a total of 560 local and foreign stamps.After giving away 80% of the local stamps and 50% of the foreign stamp, he had 172 stamps left.

a) how many local stamps did he have at first ?
b) How many foreign stamps did he give away ?

Thank you very much!!

[CoffeeCat]

YLH88:

Hi Mathsguru,


Need your help with the below question.

Yusof had a total of 560 local and foreign stamps.After giving away 80% of the local stamps and 50% of the foreign stamp, he had 172 stamps left.

a) how many local stamps did he have at first ?
b) How many foreign stamps did he give away ?

Thank you very much!!

This is a typical \"simultaneous equation\" question. The only technique tested in psle is the elimination method.

you know
20 % of local stamp + 50% of foreign stamp = 172
therefore
40% of local stamp + 100% of foreign stamp = 344
100% of local stamp + 100% of foreign stamp = 560
60% of local stamp = 560 -344 = 216
etc etc.

Alternatively you can use model to represent but the manipulation is the same.

[mathsguru]

YLH88:

Hi Mathsguru,


Need your help with the below question.

Yusof had a total of 560 local and foreign stamps.After giving away 80% of the local stamps and 50% of the foreign stamp, he had 172 stamps left.

a) how many local stamps did he have at first ?
b) How many foreign stamps did he give away ?

Thank you very much!!

Hi YLH88,

Here's my solution. Hope it helps!


MathsGuru

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

[YLH88]

Hi Mathsguru, Coffeecat,


Thank you so much!!