Q&A - PSLE Math

[pixiedust]

Appreciate any help:


Mary has 1/3 as many marbles as John. If John gives Mary 63 marbles, both of them will have an equal number of marbles. How many marbles must John give to Mary, so that Mary will have 3/4 as many marbles as John ?

[Mum1113]

pixiedust:

Appreciate any help:


Mary has 1/3 as many marbles as John. If John gives Mary 63 marbles, both of them will have an equal number of marbles. How many marbles must John give to Mary, so that Mary will have 3/4 as many marbles as John ?

Humble attempt by DS, hope it is correct

Mary:John
1 : 3 (4)
+63 -63
___________
1 : 1 (2)
2 : 2 (4)


1unit -> 63
total (4units) -> 252
252/7 = 36
36x3 = 108
63x3 = 189
189-108 = 81

Ans:81 marbles

[jieheng]

Mum1113:

pixiedust:

Appreciate any help:


Mary has 1/3 as many marbles as John. If John gives Mary 63 marbles, both of them will have an equal number of marbles. How many marbles must John give to Mary, so that Mary will have 3/4 as many marbles as John ?

Humble attempt by DS, hope it is correct

Mary:John
1 : 3 (4)
+63 -63
___________
1 : 1 (2)
2 : 2 (4)


1unit -> 63
total (4units) -> 252
252/7 = 36
36x3 = 108
63x3 = 189
189-108 = 81

Ans:81 marbles

Should be 36x4 = 144
63x3 = 189
189-144 = 45 (Ans)

OR
36x3 = 108
108-63 = 45 (Ans)

[pixiedust]

Thank you Mum1113 and jieheng.


I use back-check, ans is 45 marbles.

However, I don't understand :
1 : 3 (4)
+63 -63
___________
1 : 1 (2)
2 : 2 (4)

Is this the notation taught in school (our school haven't cover ratio yet/P5) ? Is there a solution using model ? I use model method to arrive at ans 45 but I split the problem into 2 parts and took many steps.

Thanks in advance for any help.

[tianzhu]

Hi pixiedust


Mum1113 is using a method known as the “Units Method”.It’s an alternative to MD. Unlike MD which is more visual in nature, UM is usually presented in tabulated form. There are many examples of solutions using UM in this thread.

It’s described in greater details in this book which is available in Popular.

Challenging Maths Made Easy by Ammiel Wan.

If you use MD, the first step is to find the total number of marbles.

1 unit ----- 63
4 units or the total number of marbles ------- 252

The second part is to divide 252 by 7

1 part ----- 36
Mary ------ 3 parts ------- 108

108 – 63 ------45

Best wishes

[jieheng]

pixiedust:

Thank you Mum1113 and jieheng.


I use back-check, ans is 45 marbles.

However, I don't understand :
1 : 3 (4)
+63 -63
___________
1 : 1 (2)
2 : 2 (4)

Is this the notation taught in school (our school haven't cover ratio yet/P5) ? Is there a solution using model ? I use model method to arrive at ans 45 but I split the problem into 2 parts and took many steps.

Thanks in advance for any help.

At First ,
M 1u

J 3u

Total 4u

1u -----> 63

total -----> 4u = 4*63 = 252

After John gave Mary some marbles ,
M 3u

J 4u

Total 7u

Since total units should be the same , changed the total units to the common multiples 4u*7 = 7u*4 = 28u

At First ,
M 7u (1u*7)

J 21u (3u*7)

Total 28u (4u*7)

After John gave Mary some marbles ,
M 12u (3u*4)

J 16u (4u*4)

Total 28u (7u*4)

28u -----> 252

1u -----> 9


Number of marbles that John must give to Mary = 21u - 16u = 5u = 5*9 = 45 (Ans)

[pixiedust]

Thank you for your patience everyone. Got it !

[Mum1113]

pixiedust:

Thank you for your patience everyone. Got it !

pixiedust / tianzhu / jiaheng
:oops: :oops: mistake mistake, :spank: DS later so sorrie here ...DS .must work doubly HARD

[ozora]

Need guidance.

Doris and Annie have each planned a list of words to learn,
If Doris learnt 40 words per day while Annie learnt 20 words per day, Doris would have 70 words left to learn while Annie had completed learning all the words.
If Doris learnt 20 words per day while Annie learnt 40 words per day, Doris would have 130 words left to learn while Annie had completed learning all the words.
How many words do Doris and Annie have to learn respectively?

Is my model correct? and I got stuck.

D [ 40 ][ 70]
A [20][ ]

D [20][ 130 ]
A [20][20][ ]

[MathIzzzFun]

ozora:

Need guidance.

Doris and Annie have each planned a list of words to learn,
If Doris learnt 40 words per day while Annie learnt 20 words per day, Doris would have 70 words left to learn while Annie had completed learning all the words.
If Doris learnt 20 words per day while Annie learnt 40 words per day, Doris would have 130 words left to learn while Annie had completed learning all the words.
How many words do Doris and Annie have to learn respectively?

Is my model correct? and I got stuck.

D [ 40 ][ 70]
A [20][ ]

D [20][ 130 ]
A [20][20][ ]

Hi

MD is as follows:

[] =words learnt

Scenario 1
D [][][][][70]
A [][]

Scenario 2
D [][130]
A [][]

Comparing the models for \"D\"
[][][] = 60
[] = 20

So, number of words to be learnt:
D = 4 x 20 + 70 = 150
A = 2 x 20 = 40

cheers.