Q&A - PSLE Math

[kyp71]

Hi Can anyone help to provide the solution for the below question using the model method rather than the Alegbra method ? This question is extracted from one of the parents who post up. But solution provided is in Alegbra. Please help !



At Station A, the ratio of the number of children to the number of adults on a train was 4:5. At the next station, 12 children alighted and 10 adults boarded the train. The ratio of the number of children to the number of adults on the train then become 7:10. How many children were on the train at first ?

[kyp71]

Hi Can anyone help to provide the solution for the below question using the model method rather than the Alegbra method ? This question is extracted from one of the parents who post up. But solution provided is in Alegbra. Please help !



At Station A, the ratio of the number of children to the number of adults on a train was 4:5. At the next station, 12 children alighted and 10 adults boarded the train. The ratio of the number of children to the number of adults on the train then become 7:10. How many children were on the train at first ?

[MathIzzzFun]

superworried mum:

Hi, can someone pls help in this question


There are more pens in box A than Box B. 30% of the pens in box A is 60 more than 40%
of the pens in Box B. If 5% of the pens in Box A is transferred into Box B, there will be 300 more pens in Box A than Box B.

a) How many pens are there in Box B?
b) How many percent less pens are there in Box B than Box A?

Thanks

Hi

(3/10 A = 6/20 A, 2/5 B = 6/15 B)
B --> 15u
A --> 20u+ 200

5% of A --> 1u + 10
After transfer:
B --> 16u + 10
A --> 19u + 190
A has 300 more than B
So, 19u + 190 = 16u + 10 + 300
1u --> 40

...I think you can complete the rest from here

cheers.

[peggy]

MathIzzzFun:

superworried mum:

Hi, can someone pls help in this question


There are more pens in box A than Box B. 30% of the pens in box A is 60 more than 40%
of the pens in Box B. If 5% of the pens in Box A is transferred into Box B, there will be 300 more pens in Box A than Box B.

a) How many pens are there in Box B?
b) How many percent less pens are there in Box B than Box A?

Thanks

Hi

(3/10 A = 6/20 A, 2/5 B = 6/15 B)
B --> 15u
A --> 20u+ 200

5% of A --> 1u + 10
After transfer:
B --> 16u + 10
A --> 19u + 190
A has 300 more than B
So, 19u + 190 = 16u + 10 + 300
1u --> 40

...I think you can complete the rest from here

cheers.

Hi MathIzzzfun,

Why is it A ---- 20U + 200 ? Understood for the 20U but not the 200.

Thanks.

[tianzhu]

kyp71:

Hi Can anyone help to provide the solution for the below question using the model method rather than the Alegbra method ? This question is extracted from one of the parents who post up. But solution provided is in Alegbra. Please help !



At Station A, the ratio of the number of children to the number of adults on a train was 4:5. At the next station, 12 children alighted and 10 adults boarded the train. The ratio of the number of children to the number of adults on the train then become 7:10. How many children were on the train at first ?

Hi

MD is one of the ways to solve this question.

Another approach is to use “Units and Parts”

At first
Children: Adults ------ 4 units: 5 units

Change
Children: Adults ------ -12 : 10

In the end
Children: Adults ------ 7 parts: 10 parts

Equalise the parts or cross multiply.

4 units – 12 ------- 7 parts
(x10)
40 units – 120 ------ 70 parts

5 units + 10 ------ 10 parts
(x7)
35 units + 70 ------- 70 parts

40 units – 120 ------ 35 units + 70
5 units ------- 190
1 unit ------ 38

Number of children at first ------ 38*4 ------- 152

Using MD

Due to time constraints, I'll provide some pointers instead of slide presentation.

At first
Children ------- 4 units -------8 units
Adults ------- 5 units -------- 10 units

Draw 1 box to show 1 unit.

12 children alighted
10 adults boarded

In the end
1 part ------ 1 unit (box) + 1

Children ------- 7 units + 7
Adults -------- 10 units + 10

Compare the MD for children.

7 units + 7 + 12 ------- 8 units
1 unit ------- 19

Number of children at first -------19*8 ------152

Best wishes

[MathIzzzFun]

peggy:

MathIzzzFun:

[quote=\"superworried mum\"]Hi, can someone pls help in this question


There are more pens in box A than Box B. 30% of the pens in box A is 60 more than 40%
of the pens in Box B. If 5% of the pens in Box A is transferred into Box B, there will be 300 more pens in Box A than Box B.

a) How many pens are there in Box B?
b) How many percent less pens are there in Box B than Box A?

Thanks

Hi

(3/10 A = 6/20 A, 2/5 B = 6/15 B)
B --> 15u
A --> 20u+ 200

5% of A --> 1u + 10
After transfer:
B --> 16u + 10
A --> 19u + 190
A has 300 more than B
So, 19u + 190 = 16u + 10 + 300
1u --> 40

...I think you can complete the rest from here

cheers.

Hi MathIzzzfun,

Why is it A ---- 20U + 200 ? Understood for the 20U but not the 200.

Thanks.[/quote]B--> 15u, so 40% = 6u
30% of A is 60 more than 40% of B,
So, 30% of A = 6u + 60
10% of A = 2u + 20
1005 of A = 20u + 200

cheers.

[speedmaths.012624com]

superworried mum:

Hi, can someone pls help in this question


There are more pens in A than B.
30% of the pens in A is 60 more than 40% of the pens in B.
If 5% of the pens in A is transferred into B, there will be 300 more pens in A than B.

a) How many pens are there in B?
b) How many percent less pens are there in B than A?

Thanks

Hi,

Lets try to solve this using the Advanced Model Method (or Bags and Boxes).
(Pupils used to the simple Model Method may picture / think of a Box as a Rectangle, and a Bag as a Circle)

Let there be 100 Bags (of pens) in A.
Let there be 100 Boxes (of pens) in B.

(30% of the pens in A is 60 more than 40% of the pens in B.)
30 bags = 40 Boxes + 60

(If 5% of the pens in A is transferred into B, there will be 300 more pens in A than B.)
95 bags = 100 Boxes + 5 Bags + 300
90 bags = 100 Boxes + 300

30 bags = 40 Boxes + 60
(x 3)
90 bags = 120 Boxes + 180

90 bags = 100 Boxes + 300

90 bags = 120 Boxes + 180 = 100 Boxes + 300
120 Boxes + 180 = 100 Boxes + 300
20 Boxes + 180 = 300
20 Boxes = 120
10 Boxes = 60

B = 100 Boxes = ??

90 bags = 100 Boxes + 300
90 bags = ??
10 bags = ??

A = 100 bags = ??

Can you solve from here?

Hope this helps.

The Advanced Model Method (or Bags and Boxes Method) may be found in the book Raffles Maths Tricks - Volume 1; which has been available in local book stores since 2006.

We will demonstrate this method at our Parents’ Workshop.
Please see thread on the Happenings forum.

Cheers


speedmaths.com

.

[peggy]

Please help with this CA1 from Ai Tong.


In a survey, some pupils were asked if they preferred volleyball or table tennis. 13/20 of the pupils chose volleyball, 75% of the pupils chose table tennis and 5% of the pupils did not choose any of the two sports. Given that 90 pupils chose both volleyball and table tennis, how many pupils took part in the survey ?

thank you !

[tianzhu]

peggy:

Please help with this CA1 from Ai Tong.


In a survey, some pupils were asked if they preferred volleyball or table tennis. 13/20 of the pupils chose volleyball, 75% of the pupils chose table tennis and 5% of the pupils did not choose any of the two sports. Given that 90 pupils chose both volleyball and table tennis, how many pupils took part in the survey ?

thank you !

Hi

13/20 ------ 65% ------- volleyball
75% ------- table tennis

100% - 5% ------- 95% -------- pupils who chose any of the two sports.

140% - 95% ------ 45% -------- pupils who chose both volleyball and table tennis

45% ------ 90

100% ------- 200

Best wishes

[superksmum]

Pls help with this question:


A lion and zebra were 138m apart. Upon seeing the lion, the zebra ran away from the lion at average speed of 16m/s. The lion observed the zebra for 1 minute before giving chase at an average speed of 25m/s. From the time it started giving chase, how long did the lion take to catch up with the zebra?

Thank you.