Tutor MathsGuru: Ask me for your burning Maths questions!

[acehkr3009]

tianzhu:

acehkr3009:

The ratio of Apples to Pears in a fruit stall is 5 : 8. If 60% of the pears are sold, what percentage of the apples must be sold for the number of pears and apples in the stall to be the same?

Hi

You may use MD or Units Method to solve this question.

Apples: Pears ----- 5:8 -----25:40

60% of pear% sold ----- 60/100*40 ----- 24
40% of pear left ---- (40-24) ------16

Number of apples to be sold ----- (25-16) -----9
9/25*100% ---- 36 %( percentage of apples to be sold)

Best wishes

Thanks for the answer. I fully understand now.

But for the Apples : Pear -----5:8, is there a way for choosing x5 instead of others, in order to convert to 25:40 ? If we use other factors, we may chanced upon fractions later on, which can complicate the working.

Any other method to recommend?

Thanks again.

[acehkr3009]

tianzhu:

acehkr3009:

Solution looks simple, but when I am trying it at first, brain just got stuck and freeze!

Hi

The KS way.

Keep (in) Syllabus
Keep (it) Simple
Keep (it) Short

Keep Supporting your kids

Best wishes

Hi Tianzhu,

Thanks for the KS way.....it really summarizes it all....

One of my kid has special needs (Asperger), which really require alot of attention and motivation, even though he is mathematically incline. More often, I have to built up his trust in me on the topic we doing, before I can start working with him, and to learn from each other. Thereafter, everything becomes easier and fun. So, I think Support and his interest really comes first on the list for me.

Thanks.

[ABCDE]

Kiasu Friend:

Dharma:

[quote=\"Kiasu Friend\"]

Hi tianzhu,

Thank you for the elegantly simple solution based on 'guess & check' method. But in order to understand the concept involved, can you provide a method to 'derive' the answer systematically rather than 'guessing'?

Because in the pressure of the exam-hall, 'guess & check' may be difficult to come up and quite a few wrong guesses may be tried using up precious time.

I am sorry for taking your time. Thank you very much for your tireless contribution to this forum.

Hi Kiasu Friend,

This is an alternative method for only those familiar with algebra; other wise Guess & Check is a good way to solve this problem.

40/(1u – 10) – 40/(1u + 10) = 1/6
40(20)/(1u^2 – 100) = 1/6
1u^2 – 100 = 800 x 6 = 4800
1u^2 = 4900
1u = 70

Tom’s usual speed = 1u + 10 = (70 + 10) km/h = 80km/h

Hi Dharma,

Thank you very much for the algebra solution. I can readily understand it and also somehow feel more comfortable with it.

However, as others have pointed out earlier, 'Guess & Check' seems to be a workable option that can be resorted to. But, as Tianzhu mentioned, one needs a 'number sense' to make smart guesses. I am yet to develop that skill.

Thanks and regards.[/quote]Hi Kaisu Friend,
Can u explain the algebra method used..I blur on what is 1u assumed as...
TIA

[favianboy]

2 candles A & B, A is fatter and takes 5 hours to burn. B is thinner and takes 4 hours to burn. They are the same height. At which point A is twice the height of B.


Pls help

[Kiasu Friend]

ABCDE:

Kiasu Friend:

[quote=\"Dharma\"]

Hi Kiasu Friend,

This is an alternative method for only those familiar with algebra; other wise Guess & Check is a good way to solve this problem.

40/(1u – 10) – 40/(1u + 10) = 1/6
40(20)/(1u^2 – 100) = 1/6
1u^2 – 100 = 800 x 6 = 4800
1u^2 = 4900
1u = 70

Tom’s usual speed = 1u + 10 = (70 + 10) km/h = 80km/h

Hi Dharma,

Thank you very much for the algebra solution. I can readily understand it and also somehow feel more comfortable with it.

However, as others have pointed out earlier, 'Guess & Check' seems to be a workable option that can be resorted to. But, as Tianzhu mentioned, one needs a 'number sense' to make smart guesses. I am yet to develop that skill.

Thanks and regards.

Hi Kaisu Friend,
Can u explain the algebra method used..I blur on what is 1u assumed as...
TIA[/quote]Hi ABCDE,

1u stands for the average of the two speeds, i.e., the usual speed of Tom and the slower speed at which Tom drives when he is sick.

I can explain the solution in more detail, but I think it is better that you request Dharma to explain it because:

(a) He is the author of the excellent algebra solution provided above
(b) I consider him an 'authority' on this when compared to an amateur like me.

Thanks and Regards.

[maths6a]

Dear all,

Wrt the speed qn, now that someone explained that 1u is the average of the speed he’s travelling so + 10 and -10 will be the speed he was well and sick, I can now understand the solution.

But why is it when I use
40/x - 40/x +20 = 1/6 (x being the speed when he was not well and x + 20 being the speed when he was well), then I cannot solve from here?

I think one has to be very familiar with algebra to be able to use algebra but this is like way beyond a 12 year old?

I think in this case maybe the guess and check method is a better choice especially after one has spent some time trying to work out the various possible methods?
Thanks in advance for the time to explain.

[atutor2001]

maths6a:

Dear all,

Wrt the speed qn, now that someone explained that 1u is the average of the speed he's travelling so + 10 and -10 will be the speed he was well and sick, I can now understand the solution.

But why is it when I use
40/x - 40/x +20 = 1/6 (x being the speed when he was not well and x + 20 being the speed when he was well), then I cannot solve from here?

I think one has to be very familiar with algebra to be able to use algebra but this is like way beyond a 12 year old?

I think in this case maybe the guess and check method is a better choice especially after one has spent some time trying to work out the various possible methods?
Thanks in advance for the time to explain.

You can still solve using (x+20), giving x = 60 or -80 (rejected because negative)

The use of (x+10) & (x-10) is a shortcut which only those very well versed with math will know how to capitalise, to simplify computation.

This method is beyond P6. I think Quadratic & Factorising is taught only in Sec 2. So do not spend time on it unless you are crazy over math.

[Dharma]

Kiasu Friend:

ABCDE:

[quote=\"Kiasu Friend\"]
Hi Dharma,

Thank you very much for the algebra solution. I can readily understand it and also somehow feel more comfortable with it.

However, as others have pointed out earlier, 'Guess & Check' seems to be a workable option that can be resorted to. But, as Tianzhu mentioned, one needs a 'number sense' to make smart guesses. I am yet to develop that skill.

Thanks and regards.

Hi Kaisu Friend,
Can u explain the algebra method used..I blur on what is 1u assumed as...
TIA

Hi ABCDE,

1u stands for the average of the two speeds, i.e., the usual speed of Tom and the slower speed at which Tom drives when he is sick.

I can explain the solution in more detail, but I think it is better that you request Dharma to explain it because:

(a) He is the author of the excellent algebra solution provided above
(b) I consider him an 'authority' on this when compared to an amateur like me.

Thanks and Regards.[/quote]Hi Kiasu Friend,

Please do not consider me an “authority” in maths and because I’m not one and I don’t deserve to be called that. I’m another parent just like most of you here and I am just trying to share whatever I know and at the same time learn new things here in this forum.

For the speed question, I just provided an alternative and I had qualified my solution by stating that it was meant for pupils who are familiar with algebra. Guess and check is always a great way to find the answer, if you do not know the correct method to use. For P6 kids, my advise is if you are stuck with a problem and do not know how to solve and if you resort to Guess and Check method and get the correct answer; you will get the full marks. Although, Guess and Check is not as elegant as some of the other heuristics but who cares in PSLE if your working is not elegant enough, especially when you under pressure to solve the problem that you have trouble with, don’t waste too much time thinking about the method, Guess and Check will get you the full marks (if your answer is correct). That was what I advise my dd2 last year.

Coming to the speed question, you are right that I chose 1u to be the average speed of Tom’s usual speed and Tom’s speed when he was sick.

(A + B) x (A – B) = A^2 – B^2

So,
(1u + 10)(1u – 10) = 1u^2 - 100
Then, we just find the difference in time taken when Tom was sick and when he was well (using distance divided by time) which will equal to 1/6 hour.

Solve the equation to get 1u.
To find Tom’s usual speed; you have to add 10km/h to 1u to get 80km/h

Thanks

[Herbie]

I have the following qns which needs help


SCGS
1. Mr Tan had 130 durians and mangosteens. After he sold 2/3 of the durians and 2/5 of the mangosteens. he had 36 more mangosteens than durians left. How many fruits had he left in all?

2. Tracy counted the number of 10cents coins, 20 cents coins and 50 cents coins in her piggy bank. The no. of 10cents coins was 24 more than the no. of the number of 50 cents coins. After spending 3/5 of the 10 cents coins, 1/4 of the 20 cents coins and 18 50 cents coins, she had an equal no. of 10 cents and 20 cents coins. The no. of 50 cents coins now formed 40% of the remaining number of coins.

How many 10 cents coins did Tracy have at first?
How much did she spend in all?

3. Ahmad and Halim together took 5 days o paint their house. If Ahmad and Halim work together for 2 dys, followed by Ahmad working alone for 8 days, Halim will take 1 more day to complete the remaining work. How long will Ahamd take to paint the house all by himself?

Thanks!

[Vanilla Cake]

Herbie:

I have the following qns which needs help


SCGS
1. Mr Tan had 130 durians and mangosteens. After he sold 2/3 of the durians and 2/5 of the mangosteens. he had 36 more mangosteens than durians left. How many fruits had he left in all?

2. Tracy counted the number of 10cents coins, 20 cents coins and 50 cents coins in her piggy bank. The no. of 10cents coins was 24 more than the no. of the number of 50 cents coins. After spending 3/5 of the 10 cents coins, 1/4 of the 20 cents coins and 18 50 cents coins, she had an equal no. of 10 cents and 20 cents coins. The no. of 50 cents coins now formed 40% of the remaining number of coins.

How many 10 cents coins did Tracy have at first?
How much did she spend in all?

3. Ahmad and Halim together took 5 days o paint their house. If Ahmad and Halim work together for 2 dys, followed by Ahmad working alone for 8 days, Halim will take 1 more day to complete the remaining work. How long will Ahamd take to paint the house all by himself?

Thanks!

Pls refer to this http://www.onsponge.com/forum/35-thinkingmathonsponge/3109-p6-prelim-paper-last-year-help.html#3128.