Q&A - P3 Math

[MathIzzzFun]

aps:

Hi all


Please help me with this question. I need the model approach. Thanks.

John bought some books which cost an average of $26. Two of the books cost $46 and $34 respectively. If the average cost of the remaining books was $22, find the total number of books he bought.

Hi

There is a similar question which was discussed at this thread - http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=27&t=6373&hilit=overall+average+will+be+85&start=3630

cheers.

[MathIzzzFun]

bookwormkids:

Hi MathIzzzFun!


With your model, I think I could clear my kid's query! Thanks for your help!

u r welcome.

cheers.

[whywhy]

Tin A contains some 20-cents coins and Tin B contains some 50-cents coins.

There are 9 more coins in Tin A than in Tin B.
The amount of money in Tin A is $2.70 less than that in Tin B.
How many 50-cents coins are there in Tin B ?

Is guess and check the only method to solve this Question???

[tianzhu]

whywhy:

Tin A contains some 20-cents coins and Tin B contains some 50-cents coins.

There are 9 more coins in Tin A than in Tin B.
The amount of money in Tin A is $2.70 less than that in Tin B.
How many 50-cents coins are there in Tin B ?

Is guess and check the only method to solve this Question???

Hi

Suppose or pretend that you remove 9 20 cents coins from Tin A.

9*20 ---- 180

Now Tin A has (270+180) or 450 cents less than Tin B

Difference in value between a 50 cents coin and 20 cents coin ------ 30 cents.

450/30 ------ 15

There are 15 50 cents coins in Tin B.

Best wishes

[pixiedust]

Is this P4/P5 question ?


…num of coins…*…value…Total amt of money
Tin A…U+9…20cents…20U+180
Tin B…U…50cents…50U
(…for alignment purpose)

50U = 20U + 180 + 270 = 20U + 450
30U = 450
U=15

Ans: There are 15 50-cents coins in Tin B.

---------------------------------------------------
check :
Tin B: 15 coins -> 15 x 50cents = $7.50
Tin A: 24 coins -> 24 x 20cents = $4.80
$7.50-$4.80=$2.70, checked

[pixiedust]

tianzh’s method is faster and more elegant !

[atutor2001]

1 method uses heuristic (in the past we remembered this approach as "making it equal and then working in pairs) while the other is pure mathematical approach.

I would pick the latter for the sake of future development to tackle complex problem.

[ET-PH]

atutor2001:

1 method uses heuristic (in the past we remembered this approach as \"making it equal and then working in pairs) while the other is pure mathematical approach.

I would pick the latter for the sake of future development to tackle complex problem.

The latter method uses the algebra concept, ie. let U be the number of 50 cents coins, just wonder if this is acceptable in school.

[whywhy]

Thank u all. This is a p4 question. I. will show my boy and see which method he can understand better. what abt your kids ? Heuristic or algebra method? Let’s poll n see.

[atutor2001]

ET-PH:

The latter method uses the algebra concept, ie. let U be the number of 50 cents coins, just wonder if this is acceptable in school.

Most top schools accept such method. My kids used such method more than 10 years ago (it was actually taught by one of their teachers who later became a math teacher for GEP). Yes there were complaints from some teachers but I ignore them. However, it is important to train the kids to start the question with \"Let ..... be ..U\" so that they have a good base for sec math.

The important thing is that if they don't get use to such mathematical modelling approach, it will be a nightmare solving complex problem sum. Based on what I see, the current 5 mark problems usually involve 3 unknowns. To solve with model is really tedious. Kids with know how on algebra and simultaneous can tackle them easily.