Q&A - PSLE Math

[Brenda10]

trytry:

2008

http://www.jamesangtutors.com/forum/viewtopic.php?p=5520&sid=dd197883788c1e3bdaea959288b33365

7. Mrs Smith bought some mangoes and mangosteens for $16.50. She bought 5 fewer mangoes than mangosteens. Each mango cost $1.80 more than the mangosteen. How many mangosteens did she buy?

Anyone has solution to the above question?
Crack my head can't solve.

HI,

I would like to give a try:

Mangoesteen 6 7 8 9 10

Mango 1 2 3 4 5

Additional $1.80 $3.6 $5.4 $7.2 $9


$16.5-$9= $7.5
$7.5/15 = $0.5
(10*$0.5) + (5*$2.3) = $16.50

Therefore total she bought 10 mangoesteen.

Hopefully the answer is correct.

Thanks

[atutor2001]

CoffeeCat:

To assure those who got multiple answers that they are not seeing stars...
I used the old fashioned algebra way ,
i let the marbles at first be 6x and 7x.
and the marbles added to A and B be y and 124-y respectively
using the last ratio, i form the equation
3 (6x+y) = 2( 7x+ 124-y)
i get this diophantine equation 4x + 5y = 248
the smallest solution is form when x=2, and y =48. (26 marbles at first)
the next solution is when x= 2+5 = 7 and y = 48-4 = 44 (91 marbles at first).
I stopped here but i suspect additional solutions can be obtained by adding 5 to x, and subtracting 4 from y.
It's quite late so i will digest what you said tmr morning, so it's possible i might be reading something wrongly.

Hi Coffeecat

Thanks for bring out my mistake. It is correct that there are 2 possible answers because the additional marble given was 124 (equal to 2x2x31). However, if the additional marble is 62 (equal to 2x31) then there should be only 1 answer because 1 unit will become 31 and cannot be split into any other way as 31 is a prime number.

Hi Vanilla Cake

Sorry, I cannot remember which book but it was one of those on P5 challenging math question (it is 5 years ago when my youngest kid was taking PSLE). I remember this question because I strongly disagree with it then, thinking it will generate infinite answers - until a math expert explained to me the rationale behind it.

There will be more than one answer if we use a \"composite number\" (numbers with more than 2 factors) for the additional number of marbles added to the total. This is because the marbles can then be distributed between A and B in many different ways using the different combination of factors of that \"composite number\" For the given example, the additional marble is 124 and so 1 unit is 62 = 2 x 31 or 1 x 61 allowing 2 possible answers.

As for the fact that marbles cannot be added in fraction, this limit the answer to \"whole numbers\". If instead of using marbles but let say the weight of something in kg or volume in litres, then the answers can be in fractions and there will be infinite answers as any number can be broken up into the product of 2 fractions in infinite number of ways. Hope I am right.

[trytry]

Brenda10:

trytry:

2008

http://www.jamesangtutors.com/forum/viewtopic.php?p=5520&sid=dd197883788c1e3bdaea959288b33365

7. Mrs Smith bought some mangoes and mangosteens for $16.50. She bought 5 fewer mangoes than mangosteens. Each mango cost $1.80 more than the mangosteen. How many mangosteens did she buy?

Anyone has solution to the above question?
Crack my head can't solve.

HI,

I would like to give a try:

Mangoesteen 6 7 8 9 10

Mango 1 2 3 4 5

Additional $1.80 $3.6 $5.4 $7.2 $9


$16.5-$9= $7.5
$7.5/15 = $0.5
(10*$0.5) + (5*$2.3) = $16.50

Therefore total she bought 10 mangoesteen.

Hopefully the answer is correct.

Thanks

Thanks for the solution.
You used \"guess and check\" method?
Why do you stop at 10 mangoesteen and 5 mangoes? :?

[CoffeeCat]

atutor2001:

CoffeeCat:

To assure those who got multiple answers that they are not seeing stars...
I used the old fashioned algebra way ,
i let the marbles at first be 6x and 7x.
and the marbles added to A and B be y and 124-y respectively
using the last ratio, i form the equation
3 (6x+y) = 2( 7x+ 124-y)
i get this diophantine equation 4x + 5y = 248
the smallest solution is form when x=2, and y =48. (26 marbles at first)
the next solution is when x= 2+5 = 7 and y = 48-4 = 44 (91 marbles at first).
I stopped here but i suspect additional solutions can be obtained by adding 5 to x, and subtracting 4 from y.
It's quite late so i will digest what you said tmr morning, so it's possible i might be reading something wrongly.

Hi Coffeecat

Thanks for bring out my mistake. It is correct that there are 2 possible answers because the additional marble given was 124 (equal to 2x2x31). However, if the additional marble is 62 (equal to 2x31) then there should be only 1 answer because 1 unit will become 31 and cannot be split into any other way as 31 is a prime number.

I believe you are talking about the diophantine (we call such equations diophantine because we are only interested in whole number solutions) equation
13x -5y = 62.
I understand your concern about the marbles added not being whole number, as such i formed my equation differently by defining the marbles being added as a variable.
Again let the marbles at first be 6x and 7x.
and the marbles added to A and B be y and 62-y respectively
By changing the 124 to 62 like this ... 3 (6x+y) = 2( 7x+ 124-y)
you will get 4x + 5y = 124
the smallest solution is x= 1, y=24, (13 marbles at first)
the next solution will be x= 1+5=6, y=24-4=20 (78 marbles at first).
I suspect one can get additional solutions by adding 5 to x and subtracting 4 from y.

Perhaps this is not very similar to the example you seen in the Andrew Er assessment book. It will be interesting to see that question though.
By the way no offence, it's not like I am targeting you or anything, it's a professional sickness =).

[atutor2001]

CoffeeCat:

I believe you are talking about the diophantine (we call such equations diophantine because we are only interested in whole number solutions) equation
13x -5y = 62.
I understand your concern about the marbles added not being whole number, as such i formed my equation differently by defining the marbles being added as a variable.
Again let the marbles at first be 6x and 7x.
and the marbles added to A and B be y and 62-y respectively
By changing the 124 to 62 like this ... 3 (6x+y) = 2( 7x+ 124-y)
you will get 4x + 5y = 124
the smallest solution is x= 1, y=24, (13 marbles at first)
the next solution will be x= 1+5=6, y=24-4=20 (78 marbles at first).
I suspect one can get additional solutions by adding 5 to x and subtracting 4 from y.

Perhaps this is not very similar to the example you seen in the Andrew Er assessment book. It will be interesting to see that question though.

Thank you coffeecat for confirming that I am wrong. Don't think I can find that book again or to hunt down my kid's teacher to clarify. Maybe I will go bookshop to see if I can find the assessment book.

Once again thank you for the correction.

Regards

[atutor2001]

Hi Coffeecat


Since 4x+5y can be set to be equal any number, if I change the additional marbles to 9, i.e. 4x+5y=9, then there will be only 1 solution, where x = 1 and y = 1 because negative number is not allowed.

Similarly I can change the additional marbles to 14, i.e. x=1 and y=2 and so on…

Maybe the question I saw was crafted in this way which generates only 1 solution but my explanation on "prime numbers" was definitely wrong.

Regards.

[Brenda10]

trytry:

Brenda10:

[quote=\"trytry\"]2008

http://www.jamesangtutors.com/forum/viewtopic.php?p=5520&sid=dd197883788c1e3bdaea959288b33365

7. Mrs Smith bought some mangoes and mangosteens for $16.50. She bought 5 fewer mangoes than mangosteens. Each mango cost $1.80 more than the mangosteen. How many mangosteens did she buy?

Anyone has solution to the above question?
Crack my head can't solve.

HI,

I would like to give a try:

Mangoesteen 6 7 8 9 10

Mango 1 2 3 4 5

Additional $1.80 $3.6 $5.4 $7.2 $9


$16.5-$9= $7.5
$7.5/15 = $0.5
(10*$0.5) + (5*$2.3) = $16.50

Therefore total she bought 10 mangoesteen.

Hopefully the answer is correct.

Thanks

Thanks for the solution.
You used \"guess and check\" method?
Why do you stop at 10 mangoesteen and 5 mangoes? :?[/quote]Hi trytry

When I reach the figure of 5 mangoes and 10 mangosteens (15 fruits), I continuous the verification:

5 mangoes x $1.80 = $9.00
$16.50 - $9.00 = $7.50

$7.50/15 fruits = $0.50

(15 x $0.50 + $9.00) = $16.50

The # of both fruits meet the requirement of “5 fewer” and also tally with the amount of $16.50 therefore don’t need to proceed further.

I’m not sure is there any better method but this is the best I can work out (Work in table form) since I’m also in the learning curve.

:oops:

[Vanilla Cake]

Brenda10:

trytry:

[quote=\"Brenda10\"]
HI,

I would like to give a try:

Mangoesteen 6 7 8 9 10

Mango 1 2 3 4 5

Additional $1.80 $3.6 $5.4 $7.2 $9

$16.5-$9= $7.5
$7.5/15 = $0.5
(10*$0.5) + (5*$2.3) = $16.50

Therefore total she bought 10 mangoesteen.

Hopefully the answer is correct.

Thanks

Thanks for the solution.
You used \"guess and check\" method?
Why do you stop at 10 mangoesteen and 5 mangoes? :?

Hi trytry

When I reach the figure of 5 mangoes and 10 mangosteens (15 fruits), I continuous the verification:

5 mangoes x $1.80 = $9.00
$16.50 - $9.00 = $7.50

$7.50/15 fruits = $0.50

(15 x $0.50 + $9.00) = $16.50

The # of both fruits meet the requirement of “5 fewer” and also tally with the amount of $16.50 therefore don’t need to proceed further.

I’m not sure is there any better method but this is the best I can work out (Work in table form) since I’m also in the learning curve.

:oops:[/quote]Hi Brenda10,
Pls refer to the http://psle2010a.blogspot.com/2010/05/decimal-p5.html by Uncle Observer. Depending on how you interpret the question, it seems that this question has multiple answers like the marble question posted by http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=11112&start=20.

Hi trytry,
Why don't you ask http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=6611 directly for the solutions from his http://www.jamesangtutors.com/forum/viewtopic.php?p=5520&sid=dd197883788c1e3bdaea959288b33365 instead of \"Crack my head can't solve.\"
BTW, Uncle Observer had provided all the solutions for the 8 questions in his http://psle2010a.blogspot.com/ on Monday, 24 May 2010.So, readers may wish to go through the questions as well as the solutions provided by the kind and helpful Uncle Observer.

[Maths Monster]

delete

[Brenda10]

Hi Vanilla Cake and Maths Monster,


Thank you for your highlight and we can learn to be more alert in future.


BTW, if this is the exam question, do we have to provide two sets of answer?

Thank you.