Tutor MathsGuru: Ask me for your burning Maths questions!

[mathsguru]

YLH88:

Hi Mathsguru,


Need your help in the following questions :

1) In a mathematics competition with 100 participants, the average score was 63. Given that the average score of the boys was 60 and that of the girls was 70, find the number of boys and that of girls who participated in the competition.

2) Tom's present age is thrice Sally's age some years ago. Conversely, Sally's present age is Tom's age the same number of years ago. Given that the sum of their present ages is 30 years, how old is Tom now ?

3) When Kok Hwa's age was twice Bala's age, Mike's age was 30. When MIke's age was twice Kok Hwa's age, Bala's age was 21. Given that Mike was the oldest among the three persons, find Bala's age when Mike was 62 years old.

Thank you very much

Hi YLH88,

Here are my solutions.

http://www.postimage.org/image.php?v=gxeRI1A

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

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

Cheers,
MathsGuru

[mathsguru]

pokemon:

Muffins:

Hi pokemon, I haven't forgotten ( :x ) but, I understand your son's method as I use algebra to solve problems, though mathsguru uses models.

Talk about using algebra, some questions my son will sort of use algebra method though nobody taught him :? , even my elder sec sch son also said the same like you. My elder boy v happy now cos in sec sch no need to use model,juz apply algebra.

Actually, to a certain extent, model diagrams used in those challenging problems (esp. ratio/fractions) are in essence simultaneous equations at work!

Just try to notice it the next time you encounter the more \"complex\" diagrams. For e.g. whenever we express 1 item in terms of another item, we are actually doing substitution method (in algebra), just that it's easier for primary school students to \"visualise\" with the aid of diagrams than to use \"x\" and \"y\"...

My 2 cents' worth,
MathsGuru

[YLH88]

Hi Mathsguru,


Thank you very much for your prompt reply.

But hor, don’t quite understand the solution for question 2. I don’t understand how you get the 3rd set of diagram with the yellow box. How come is 1/3 of Tom’s present age ? and how to get the 5 units ?

Many thanks!

Regards
Jasmine

[thinkingmath]

YLH88:

1) In a mathematics competition with 100 participants, the average score was 63. Given that the average score of the boys was 60 and that of the girls was 70, find the number of boys and that of girls who participated in the competition.

Hi YLH88

Another method removing \"the guess work\" that we sometimes teach our students is using a method we call Number of Units x Value of Units. Our P3 books introduce this method very successfully, however, most questions would not have negative numbers involved. Given this is related to Average, this question will be at least P5 and at this Level our students will have no problem using Number of Units x Value of Units for this question. The advantage is that it removes any guess work and is an more efficient approach.

http://www.onsponge.com/pub_images/onsponge_number_value_20100120.jpg\">

[Dharma]

YLH888,


This is another approach to solve the age problem.

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

[YLH88]

Hi Dharma, Thinkingmath


Thank you very much !!

Regards

[i-mum]

Hi MathsGuru, I have a question:


Mani and Muthu have some amount of money. If Muthu gives Main $40, they will each have the same amount of money. If Mani give Muthu $120, Muthu will have 3 times as much as Mani. How much does Mani and Muthu have?

[mathsguru]

YLH88:

Hi Mathsguru,


Thank you very much for your prompt reply.

But hor, don't quite understand the solution for question 2. I don't understand how you get the 3rd set of diagram with the yellow box. How come is 1/3 of Tom's present age ? and how to get the 5 units ?

Many thanks!

Regards
Jasmine

Hi Jasmine,

As mentioned, the yellow box represents the no. of years that have passed, which means Sally's present age minus away the yellow box = Sally's age then. Similarly, Tom's present age minus away the yellow box = Tom's age then.

Based on this, we can \"divide\" Sally's present age (from the 2nd set of diagram) into her age then + the no. of years that have passed. This will mean that the pink diagram should include the yellow box, that's why you find that I've\"inserted\" the yellow box into her present age diagram. The remaining pink box will represent her age then.

Since Tom's age then is equal to Sally's present age, it should be of the same size as the remaining pink box + yellow box. Next, using the information from the 1st set of diagram, we know that Tom's present age is 3 times that of Sally's age then. To obtain Tom's present age, simply add a yellow box behind as that is the no. of years that has passed.

Finally, for Tom's present age to be 3 times of Sally's age then (the remaining pink box), it is only logical to conclude that Sally's age then (the remaining pink box) is equal to the yellow box.

Therefore, Sally's present age is equal to 2 units while Tom's present age is equal to 3 units. Total = 5 units. Since we know their present ages add up to 30, 5 units = 30.

Hope my explanation above is clear enough for you to understand... Pls feel free to clarify if needed.

Cheers,
MathsGuru

[mathsguru]

i-mum:

Hi MathsGuru, I have a question:


Mani and Muthu have some amount of money. If Muthu gives Main $40, they will each have the same amount of money. If Mani give Muthu $120, Muthu will have 3 times as much as Mani. How much does Mani and Muthu have?

Hi i-mum,

Here's my solution.

http://www.postimage.org/image.php?v=aV1FddeA

Cheers,
MathsGuru

[YLH88]

Hi Mathsguru,


Need your help again to solve the following questions. These 2 questions are under the Algebra unit.

1) A certain amount of water is poured from a jug into an empty mug so that the amount of water in the mug is 1/6 the amount of water left in the jug. If 50 ml of water is further poured from the jug to the mug, the amount of water in the mug will be 1/5 of that left in the jug.
Find the original amount of water in the jug.


2) Meatballs and fishballs were sold in packets. Each packet contained the same number of meatballs and fishballs. Meatballs were priced at 4 pieces at $1 and fishball at 6 pieces for $1. A man had just enough money to buy 2 packets of meatballs and 1 packet of fishballs. He needed one more dollar if he were to buy 3 packets of meatballs instead. Find the number of meatballs or fishballs in a packet.


Thank you!