Q&A - PSLE Math

[Musicstar]

Hi oldschool,

Can help to explain why 5-4 = 3-2=7 yrs. I still do not understand. is it must make both ratio diff of 1. Sorry , maybe my english not good cannot understand .

quote=\"Oldschool\"]

Musicstar:

Why the ratio for 7 years ago change to 4 : 2?

Hi,

So that the difference between now and 7 years ago is the same for both boys.

i.e. 5-4 = 3-2 = 7 years.

Regards[/quote]

[MathIzzzFun]

Musicstar:

Hi,


Can someone help to check whether this question any problem? I have the answer but still do not understand . Why the ratio for 7 years ago change to 4 : 2?



Question:
Seven years ago, the ratio of the Samuel's age to George's age was 2: 1. The ratio of their ages is 5 : 3 this year. What will be the ratio of their ages in seven years time?

Answer:
7 years ago
S : G
2 : 1
4 : 2

Now
S : G
5 : 3

diff 5 -4 =1
1u = 7
5u = 5 x 7
= 35
3u = 3 x 7
=21
Samuel is 35 yrs old & George is 21 yrs old.

7 years time
s : G
35 + 7 = 42 21 + 7 = 28
3 : 2
The ratio of their ages wil be 3: 2

For questions on age.... the key concept is - ‘age difference or age gap will remain the same’

in the first ratio 2:1, difference -> 2-1= 1
in the second ratio 5:3, difference -> 5-3 = 2

since age difference must remain the same, first ratio is doubled --> 4:2, so difference -> 4-2 = 2
which is now equal to difference in the second ratio.

cheers.

[tianzhu]

Musicstar:

Can help to explain why 5-4 = 3-2=7 yrs. I still do not understand. is it must make both ratio diff of 1.

Hi

Good Morning

PapayaDad has shown one way of solving your question using UP.Some students may prefer to use it because it gives them a standard way of solving many \"before and after scenario type of questions\".

As for the answer presented in your post, it actually makes use of equivalent ratios taking into consideration that the difference in age between Samuel and George stays the same.

If you compare the units;

7 years ago
Samuel ----- 4u
George ----- 2u

This Year
Samuel ----- 5u
George ----- 3u

You may choose to use the unit for Samuel or George as the difference in their age stays the same (7).

You may use 5 - 4 --- 1 or 3 - 2 --- 1.

There are different ways to present the solution, I've shown one one way.Choose the format your kid is comfortable with.

Hope this helps.

Best wishes

http://farm9.staticflickr.com/8116/8640747153_e7148d4293_z.jpg\">

[Musicstar]

Wow. Finally, I have understand . :thankyou:

MathIzzzFun:

Musicstar:

Hi,

Can someone help to check whether this question any problem? I have the answer but still do not understand . Why the ratio for 7 years ago change to 4 : 2?



Question:
Seven years ago, the ratio of the Samuel's age to George's age was 2: 1. The ratio of their ages is 5 : 3 this year. What will be the ratio of their ages in seven years time?

Answer:
7 years ago
S : G
2 : 1
4 : 2

Now
S : G
5 : 3

diff 5 -4 =1
1u = 7
5u = 5 x 7
= 35
3u = 3 x 7
=21
Samuel is 35 yrs old & George is 21 yrs old.

7 years time
s : G
35 + 7 = 42 21 + 7 = 28
3 : 2
The ratio of their ages wil be 3: 2

For questions on age.... the key concept is - ‘age difference or age gap will remain the same’

in the first ratio 2:1, difference -> 2-1= 1
in the second ratio 5:3, difference -> 5-3 = 2

since age difference must remain the same, first ratio is doubled --> 4:2, so difference -> 4-2 = 2
which is now equal to difference in the second ratio.

cheers.

[rocklee]

Hi Tianzhu


Yesterday, my son came back with a few challenging questions involving the units and parts method. It took me an hour to help solve all of them. These questions could have been solved within minutes using algebra. Unfortunately, kids are not taught using 2 variables. Hence, I have to go figure out what this "units and parts method" is all about. No wonder parents and kids get so stressed up nowadays.

This thread has more than 800 pages. I wonder if you have by chance helped solve the "Double IFs’ type of questions? Is yes, appreciate if you could direct me to those pages.

Million thanks.

[Musicstar]

Thank you Tianzhu. I like your picture below. It is colourful , good illustration and with panda photo which my girl likes it very much.

quote=\"tianzhu\"]

Musicstar:

Can help to explain why 5-4 = 3-2=7 yrs. I still do not understand. is it must make both ratio diff of 1.

Hi

Good Morning

PapayaDad has shown one way of solving your question using UP.Some students may prefer to use it because it gives them a standard way of solving many \"before and after scenario type of questions\".

As for the answer presented in your post, it actually makes use of equivalent ratios taking into consideration that the difference in age between Samuel and George stays the same.

If you compare the units;

7 years ago
Samuel ----- 4u
George ----- 2u

This Year
Samuel ----- 5u
George ----- 3u

You may choose to use the unit for Samuel or George as the difference in their age stays the same (7).

You may use 5 - 4 --- 1 or 3 - 2 --- 1.

There are different ways to present the solution, I've shown one one way.Choose the format your kid is comfortable with.

Hope this helps.

Best wishes

http://farm9.staticflickr.com/8116/8640747153_e7148d4293_z.jpg\">[/quote]

[PapayaDad]

Hi tianzhu,


I learn from your blog too. Thanks a lot.

rocklee,

You may want to check out the blog too :

http://www.kiasuparents.com/kiasu/content/math-questions-involving-two-changed-quantities

[Oldschool]

Musicstar:

Hi oldschool,

Can help to explain why 5-4 = 3-2=7 yrs. I still do not understand. is it must make both ratio diff of 1. Sorry , maybe my english not good cannot understand .

Hi,

Sorry for not been clearer.

To add further,

a) the age difference between Sam and George is always the same no matter how old or young they are.

e.g. If Sam is born in 1990 and George in 2000, their age difference is always 10.

b) the age difference between now (2013) and 7 years ago (2006) is the same for everybody. i.e. 7 years.

Regards

[tianzhu]

rocklee:

Hi Tianzhu


Yesterday, my son came back with a few challenging questions involving the units and parts method. It took me an hour to help solve all of them. These questions could have been solved within minutes using algebra. Unfortunately, kids are not taught using 2 variables. Hence, I have to go figure out what this \"units and parts method\" is all about. No wonder parents and kids get so stressed up nowadays.

This thread has more than 800 pages. I wonder if you have by chance helped solve the \"Double IFs' type of questions? Is yes, appreciate if you could direct me to those pages.

Million thanks.

Hi

Actually, there are two variables in UP, units and parts. Students are dealing with two equations, but it is packaged that in such a way that it looks less frightening to kids.

Before I go on, I must say I am a post PSLE dad, which means I’ve not been reading the latest books or past years papers for the last few years already.

I may not be able to give you examples of the latest trend of exam questions, if any.

Let me search through some slides of the past years questions on two ifs I had done tomorrow afternoon.

I’ll PM to you by Mon afternoon.

Best wishes

[ozora]

Apologies for repeated request

\t
Need some guide for this age question.
When Mrs Sam was 40 years old, her son was twice her daughter’s age.
Mrs Sam would be twice her son’s age when her daughter was 28 years old.
How old would Mrs Sam be when her daughter was 20 years old?
I got the answer of 56 using algebra and using model.
Anymore other alternative?