Tutor MathsGuru: Ask me for your burning Maths questions!

[speedmaths.012624com]

Vanilla Cake:

Hi Mathsguru,

Pls help my P5 younger sister to solve this 4-mark question from http://www.orlesson.org/orp/09Ma/2009-Math-SA1-ACS.pdf using models. Thank you.

The volume of water in bottle P was 3/5 of that in bottle Q. After 60 ml of water was added to bottle P and 20 ml was poured away from bottle Q, the amount of water in bottle P was 3/4 that in bottle Q. What was the amount in each bottle at first?

Other than models, what are your recommended method/s to tackle such problem sum?

Hi Vanilla Cake,

The volume of water in bottle P was 3/5 of that in bottle Q.
After 60 ml of water was added to bottle P and 20 ml was poured away from bottle Q, the amount of water in bottle P was 3/4 that in bottle Q.
What was the amount in each bottle at first?

Let’s CHANGE the question (but still using the SAME numbers) to:

In a shop, the ratio of the number of apples to the number of oranges was 3:5, at first.
The shopkeeper bought 60 more apples, and sold 20 oranges.
As a result, the ratio of the number of apples to the number of oranges became 3:4.
How many apples and how many oranges, were there in the shop at first?

This is a typical Double-Ratio Question, quite common in the PSLE.

Using the Bags and Boxes Method (which can solve ALL such Double-Ratio Questions):
(Once you are familiar with the method, you can cut down some of the steps below)


At first, the apples / oranges were kept in Bags.
Each Bag contains the same number of apples / oranges.
There were 3 Bags of apples, and 5 Bags of oranges, at first.

After 60 apples were added, and 20 oranges were removed,
the apples / oranges were then kept in Boxes.
Each Box contains the same number of apples / oranges.
There were 3 Boxes of apples, and 4 Boxes of oranges.

Apples:
3 bags + 60 apples = 3 Boxes
(x 4)
12 bags + 240 apples = 12 Boxes

Oranges:
5 bags – 20 oranges = 4 Boxes
(x 3)
15 bags – 60 oranges = 12 Boxes

12 Boxes = 12 bags + 240 apples = 15 bags – 60 oranges
12 bags + 240 apples = 15 bags – 60 oranges
0 bags + 240 apples = 3 bags – 60 oranges
240 apples = 3 bags – 60 oranges
300 apples / oranges = 3 bags
1 Bag = 100 apples / oranges
There were 3 Bags of apples, and 5 Bags of oranges, at first.

There were 300 apples, and 500 oranges, at first. (ANSWER)

[Dharma]

Vanilla Cake:

Hi Mathsguru,

Pls help my P5 younger sister to solve this 4-mark question from http://www.orlesson.org/orp/09Ma/2009-Math-SA1-ACS.pdf using models. Thank you.

The volume of water in bottle P was 3/5 of that in bottle Q. After 60 ml of water was added to bottle P and 20 ml was poured away from bottle Q, the amount of water in bottle P was 3/4 that in bottle Q. What was the amount in each bottle at first?

Other than models, what are your recommended method/s to tackle such problem sum?

Hi Vanilla Cake,

Your sister may wish to look at this while waiting for Mathsguru’s solution.


http://www.postimage.org/image.php?v=gxEDrbJ

[OK Lor]

Hi Mathsguru,


The product of two numbers, A and B, is 108. The difference betweeen A and B is a common factor of A and B. Find the values of A and B.

Thanks.

[Dharma]

OK Lor:

Hi Mathsguru,


The product of two numbers, A and B, is 108. The difference betweeen A and B is a common factor of A and B. Find the values of A and B.

Thanks.

108 = 2 X 2 X 3 X 3 X 3 = 12 X 9
A = 12, B = 9 (A – B = 12- 9 = 3)
3 is a common factor of both 12 and 9.

[Herbie]

Hi, Maths Guru and all


Can help to solve the qn below?

Amy and Tommy each have some money. If Amy spends $50 per day and Tommy spends $60 per day, Amy would still have $500 left when Tommy has spent all his money.
If Amy spends $60 per day and Tommy spends $50 per day, Amy would still have $280 left when Tommy spent al his money. How much money does Tommy have?

Tx

[ck123]

Hi all


I need help with the model for this question.

The number of marbles in Box A, Box B and Box C was 195.
John added 60 marbles to those in Box A, doubled the number of marbles in Box B and halved the number of marbles in Box C.
The ratio of the number of marbles becomes 4:1:2.
What is the total number of marbles in the three boxes now?

Thanks

[Vanilla Cake]

Herbie:

Amy and Tommy each have some money. If Amy spends $50 per day and Tommy spends $60 per day, Amy would still have $500 left when Tommy has spent all his money.

If Amy spends $60 per day and Tommy spends $50 per day, Amy would still have $280 left when Tommy spent al his money. How much money does Tommy have?

Hi Herbie,
Your question is similar to this http://www.postimage.org/image.php?v=gxtwwpi which Mathsguru had provided clear explanations.

1st case
Amy : Tommy
5 : 6
25 : 30

2nd case
Amy : Tommy
6 : 5
36 : 30

Draw models for better visualisation,
1st case
Amy: 25 units + a long block to indicate $500 left
Tommy : 30 units

2nd case
Amy: 36 units + a long block to indicate $280 left
Tommy: 30 units

Make sure that total length of both blocks for Amy in 1st/2nd case must be the same.

25 units+$500=36 units+$280
11 units = $220
1 unit = $20

Tommy has 30 units = $600

Check
1st case - 10 days
Amy -> $1000-(10x$50) = $500
Tommy=> $600-(10x60) = 0

2nd case - 12 days
Amy -> $1000-(12x60) = $280
Tommy -> $600-(12x50) = 0

[Vanilla Cake]

Dharma:

Hi Vanilla Cake,


Your sister may wish to look at this while waiting for Mathsguru’s solution.

http://www.postimage.org/image.php?v=gxEDrbJ

Hi Dharma,
Thanks for your effort and time. Your alternative approach is the same method that I had taught her but she wants to learn the model solution by Mathsguru.

Hi Guan Hui/speedmaths.com,
Thanks for your solutions.

Hi Mathsguru,
From http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=6113&postdays=0&postorder=asc&start=100 and his http://chillycrab.webs.com/, is it possible for you to compile all your questions and solutions from this thread into a blog/website for others to learn from you?

[Vanilla Cake]

ck123:

I need help with the model for this question.


The number of marbles in Box A, Box B and Box C was 195.
John added 60 marbles to those in Box A, doubled the number of marbles in Box B and halved the number of marbles in Box C.
The ratio of the number of marbles becomes 4:1:2.
What is the total number of marbles in the three boxes now?

Hi ck123,
Thank you for posting this http://www.orlesson.org/orp/09Ma/2009-Math-SA1-RGS.pdf.My P5 younger sister also cannot understand the given worked solution.

While waiting for help, please see whether my method is useful or not?
Draw the model for \"after\" scenario:

After
Box A : 8 equal blocks
Box B : 2 equal blocks
Box C : 4 equal blocks

Before
Box A : 8 equal blocks - 60
Box B : 1 block
Box C : 8 equal blocks

8 blocks-60+1 block+8 blocks = 195
17 blocks = 255
1 block = 15

1 block is the same as 1 unit

Total marbles in the three boxes now : (8+2+4) blocks = 14 blocks
14 blocks = 14x15 = 210

Mod : Pls merge this thread with http://www.kiasuparents.com/kiasu/forum/viewtopic.php?p=160403#160403 so that Mathsguru can post a clear and well-illustrated model solution.

Thanks.

[OK Lor]

Dharma:

OK Lor:

Hi Mathsguru,


The product of two numbers, A and B, is 108. The difference betweeen A and B is a common factor of A and B. Find the values of A and B.

Thanks.

108 = 2 X 2 X 3 X 3 X 3 = 12 X 9
A = 12, B = 9 (A – B = 12- 9 = 3)
3 is a common factor of both 12 and 9.

Hi Dharma,

Thanks.