Q&A - PSLE Math

[happyheart]

MathIzzzFun:

happyheart:

Hi, one more please. I am always confused when there is transfer back and forth.Thanks.


Jack and Aqil had some game cards. If Jack gave Aqil 52 cards, he would have the same number of cards as Aqil. If Aqil gave Jack 34 cards, the ratio of the number of cards Aqil had to the number of cards Jack had would be 3:7.How many cards did Jack have at first?

If Jack gave Aqil 52 cards, he would have the same number of cards as Aqil
--> Jack has 52 x 2 = 104 more cards than Aqil at first.

If Aqil gave Jack 34 cards,
--> Jack would have 104 + 34 x 2 = 172 more cards than Aqil

So, 4u --> 172, 1u --> 43
Number of cards Jack has at first = 7 x 43 - 34 = 267

cheers.

Thank you, MathIzzzFun.

[happyheart]

Jwoofamily:

Use model.


If jack give aqil 52 cards and they have same number means the model is like this.

J [ ][ 52 ][ 52 ]
A [ ]

If A gives 34 to J, the model will be as shown below whereby 34+34+52+52=4 units.

J [][][][34][34][ 52 ][ 52 ]
A [][][]

Find 1 unit and you can find solve the problem by tracing back to the original quantity.

Thank you, Jwoofamily.

[happyheart]

MathIzzzFun:

happyheart:

Hi,

pls help with this question. Thanks!

Andy, Brad, Colin shared money to buya present for their teacher. The ratio of the amount of money contributed by Andy to the total amount contributed by Brad, Colin and Dominic was 1:5. Brad contributed 1/11as much as the total contributed by Dominic. If Andy contributed $2.10 more than Brad, how much did Dominic contribute?

...seems that some info was left out ??

Soorry!! :imsorry: I rechecked the question and it should be phrased like this.


Andy, Brad, Colin shared money to buy a present for their teacher. The ratio of the amount of money contributed by Andy to the total amount contributed by Brad, Colin and Dominic was 1:5. Brad contributed 1/11 as much as the total contributed by Andy, Colin and Dominic. Colin contributed 4/5 of the amount contributed by Dominic. If Andy contributed $2.10 more than Brad, how much did Dominic contribute?

[happyheart]

cimman:

happyheart:

Hi, one more please. I am always confused when there is transfer back and forth.Thanks.


Jack and Aqil had some game cards. If Jack gave Aqil 52 cards, he would have the same number of cards as Aqil. If Aqil gave Jack 34 cards, the ratio of the number of cards Aqil had to the number of cards Jack had would be 3:7.How many cards did Jack have at first?

actually, you should see this as a Double If question rather than a back and forth transfer question. Double If question is easy to recognize because there are 2 Ifs in the question. The key thing to note in Double If question is the starting point (Before) is the same in both If cases. Work your way up to the Before values in both cases (each If statement is a case) and equate them together.

Thanks Cimman. Somehow I cannot see the question like you :scratchhead: I see the question more like one person give something to another and return back to the same person etc. I am lost by the second transfer and cannot draw the model correctly. MathIzzzfun and Tianzhu has kindly showed the way to solve this question.

[MathIzzzFun]

happyheart:

MathIzzzFun:

[quote=\"happyheart\"]Hi,

pls help with this question. Thanks!

Andy, Brad, Colin shared money to buya present for their teacher. The ratio of the amount of money contributed by Andy to the total amount contributed by Brad, Colin and Dominic was 1:5. Brad contributed 1/11as much as the total contributed by Dominic. If Andy contributed $2.10 more than Brad, how much did Dominic contribute?

...seems that some info was left out ??

Soorry!! :imsorry: I rechecked the question and it should be phrased like this.


Andy, Brad, Colin shared money to buy a present for their teacher. The ratio of the amount of money contributed by Andy to the total amount contributed by Brad, Colin and Dominic was 1:5. Brad contributed 1/11 as much as the total contributed by Andy, Colin and Dominic. Colin contributed 4/5 of the amount contributed by Dominic. If Andy contributed $2.10 more than Brad, how much did Dominic contribute?[/quote]Total amount of money remains the same,
Brad : Andy, Colin & Dominic : Total -> 1u : 11u : 12u

Andy : Brad, Colin & Dominic : Total = 1 : 5 : 6 -> 2u : 10u : 12u

Andy : Brad : Total : Colin & Dominic
--> 2u : 1u : 12u : 9u (= 12u - 2u -1u)

Colin : Dominic : Colin & Dominic --> 4u : 5u : 9u

Andy : Brad: Colin : Dominic --> 2u : 1u : 4u : 5u

Andy contributed $2.10 more than Brad,
2u - 1u = 1u --> $2.10

Dominic's contribution --> 5 x $2.10 = $10.50

cheers.

[happyheart]

MathIzzzfun, Thank you for your help.

[SAHMwith2boys]

Can someone help with the below question:

http://i46.tinypic.com/14qyd3.jpg\">

It's taken from 2012 CHIJ CA1 paper.

[MathIzzzFun]

SAHMwith2boys:

Can someone help with the below question:

http://i46.tinypic.com/14qyd3.jpg\">

It's taken from 2012 CHIJ CA1 paper.

http://i48.tinypic.com/hvqj42.png\">

cheers.

[SAHMwith2boys]

MathIzzzFun:

SAHMwith2boys:

Can someone help with the below question:

http://i46.tinypic.com/14qyd3.jpg\">

It's taken from 2012 CHIJ CA1 paper.

http://i48.tinypic.com/hvqj42.png\">

cheers.

This method seems a bit tough for Primary level, was wondering is there any other way to do this?

[MathIzzzFun]

SAHMwith2boys:

MathIzzzFun:

[quote=\"SAHMwith2boys\"]Can someone help with the below question:

http://i46.tinypic.com/14qyd3.jpg\">

It's taken from 2012 CHIJ CA1 paper.

http://i48.tinypic.com/hvqj42.png\">

cheers.

This method seems a bit tough for Primary level, was wondering is there any other way to do this? [/quote]The solution is not beyond P6 students.

2 key information are provided - triangle ABC is isosceles and angle AGE = 75 deg. So, one has to made use of these to work out the solution.

another approach is to work out the angle CAG in terms of the angles EFC and FCA and then use the interior angles of quadrilateral ACFG to work out angle FCA (1u)

angle CAG = 180 -(90-1u) = 1u + 90
in quadrilateral ACFG
angle EFC + angle FCA + angle CAG + angle AGE = 360
2u + 1u + 1u + 90 + 75 = 360
4u = 195, 1u = 48.75

http://i45.tinypic.com/qstohc.png\">

cheers.