Q&A - PSLE Math

[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

[PapayaDad]

wow… i am learning too… good one oldschool!

[Oracle]

Thanks MathIzzzFun, it’s legible but sorry still could not see the relationship of the 1 unit being 24 km. Also, what’s the significance of the 1 unit?

[tianzhu]

Oracle:

3. Ann left Town A for Town B. At the same time, Ben left Town B for Town A. Ann drove at an average speed of 72 km/hr while Ben drove at 56 km/h. Ann and Ben passed each other at a point 24 km from the mid point of Towns A and B. What is the distance between A and B?

Hi

Another way of looking at this question as discussed earlier in this thread.

When two cars are travelling in opposite directions, the sum of individual distances in equal to the total distance between them.

There are a few approaches to this question.

It helps to start with a simple diagram.

In 1h, A and B covered 128 km (56+72).

In 1h, they passed each other at 8 km from the midpoint, 64km (128/2)

8km ----- 1h

24km ------- 3h

Therefore in 3h, they are 24km from the midpoint.

Distance between A and B ------- 3*128 ------ 384 km.

Best wishes

[MathIzzzFun]

Oracle:

Thanks MathIzzzFun, it's legible but sorry still could not see the relationship of the 1 unit being 24 km. Also, what's the significance of the 1 unit?

Ann left Town A for Town B. At the same time, Ben left Town B for Town A. Ann drove at an average speed of 72 km/hr while Ben drove at 56 km/h. Ann and Ben passed each other at a point 24 km from the mid point of Towns A and B. What is the distance between A and B?

Ann's speed : Ben's speed = 72 : 56 --> 9 : 7

When Ann and Ben passed each other,
Ann has travelled a distance of 9 units from Town A, and
Ben has travelled a distance of 7 units from Town B

Total distance between Town A and Town B --> 9 units + 7 units = 16 units

mid point between town A and town B
= 8 units from Town A
= 8 units from Town B

Since Ann travelled a distance of 9 units from Town A,
Ann has travelled 9 units - 8 units = 1 unit past midpoint between A and B

Similarly, since Ben has travelled 7 units from Town B,
Ben has travelled 8 units - 7 units = 1 unit away (before) the midpoint between A and B.

So, 1 unit --> 24 km
Distance between A and B = 16 x 24 km = 384 km

cheers.

[ozora]

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?

[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.