Tutor MathsGuru: Ask me for your burning Maths questions!

[Tang]

Vanilla Cake:

CoffeeCat:

i think vanilla is hoping for mathsguru to come up with an alternative solution based on models.

Yes, CoffeeCat. You are right, I am looking for alternative solution based on models from Mathsguru besides the solution using simultaneous equations as posted by Tang.

Hi Vanilla Cake,

I believe this is the model drawing you are looking for.


http://psle2010a.blogspot.com/2010/03/percentage_24.html


Hope it is useful for Pandan Cake.

[Vanilla Cake]

firebird:

1) Sophie and Rachel share blue ribbons in the ratio of 5 : 2.They want to buy some red ribbons so that the total number of ribbons they have will be tripled. In what ratio must they divide the red ribbons so that Rachel will have twice the number of ribbons she has now?

A1

Before
S : R
5 : 2

Total->5+2=7.
To buy additional red ribbons so that the total number of ribbons will be tripled means 7x3=21.

After
S : R
17 : 4 (Rachel will have twice the number of ribbons->2x2=4, remainder will be 21-4=17 for Sophie)

For Sophie: (17-5) units = 12 units
For Rachel: (4-2) units = 2 units

12: 2 = 6:1
Ratio for them to divide the red ribbons is 6:1

firebird:

2) Faizal has a rod. He needs 6 minutes to saw it into 4 pieces. How many minutes does he need to saw the rod into 28 pieces?

A2

To get 4 pieces of the rod, Faizal needs to saw 3 times.
To get 28 pieces of the rod, Faizal needs to saw 27 times.

To saw the rod for 3 times -> 6 minutes
To saw the rod for 27 times -> 27/3x6 = 9x6 = 54 minutes

Faizal will need 54 minutes to saw the rod into 28 pieces.

firebird:

3) Customers were given a free CD for every 2 CDs they buy at a sale.Ben spent $K and got 30 CDs in all. What is the price of 1 CD?

A3

30/(2+1)x2 = 20 means 20 CDs are bought and 10 CDs were given free.
Total amount that Ben spent was $K.
Price of 1 CD = $(K/20)

firebird:

4) There were some horses and people on a farm. There were 62 more legs than heads. There were 26 more heads than tails.
a) How many people were there?
b) How many horses were there?

A4
There were 26 more people than the horses.
(Horse : 1 head + 1 tail)
(Person: 1 head only)

Head
Horse : unit
People : unit +26

Legs
Horses : 4 units
People : 2 units +52

Total heads : 2 units + 26
Total legs : 6 units + 52

6 units+52-(2 units+26) = 62 (Given that 62 more legs than heads)
6 units+52-2 units-26=62
4 units+26=62
4 units = 36
1 unit = 9

(a) Number of people would be 26+9 = 35
(b) Number of horses would be 9

firebird:

5) Sugar and water are mixed in the ratio 1:5 to make syrup. The volume of the syrup is 800 cm³

a) Find the volume of sugar in the syrup.
b) Find the volume of water in the syrup.
c) How much more sugar must be added to the surup so that the ratio of the sugar to water in the syrup becomes 1:3?

A5
S : W
1 : 5

6 units = 800 cm³
1 unit = (800/6) cm³ = 133⅓ cm³

(a) Volume of sugar in the syrup is 133⅓ cm³

(b) Volume of water in the syrup will be 5x133⅓ cm³ = 666⅔ cm³

Before
S : W
1 : 5
3 : 15

After
S : W
1 : 3
5 : 15

There is no change for the water as only sugar is added to the syrup.

3 units = 133⅓ cm³
2 units = 88 8/9 cm³

(c) Additional sugar to be added is 88 8/9 cm³

Hope this helps while waiting for Mathsguru to provide her solutions.

[Vanilla Cake]

Tang:

Vanilla Cake:

[quote=\"CoffeeCat\"]i think vanilla is hoping for mathsguru to come up with an alternative solution based on models.

Yes, CoffeeCat. You are right, I am looking for alternative solution based on models from Mathsguru besides the solution using simultaneous equations as posted by Tang.

Hi Vanilla Cake,
I believe this is the model drawing you are looking for.

http://psle2010a.blogspot.com/2010/03/percentage_24.html

Hope it is useful for Pandan Cake.[/quote]Hi Tang,
Thanks for your link. That's the problem with Pandan Cake as she is afraid that she may lose marks in Maths exams if she does not use model solutions to solve.

:love:

[Tang]

firebird:

4) There were some horses and people on a farm. There were 62 more legs than heads. There were 26 more heads than tails.

a) How many people were there?
b) How many horses were there?

I really do not know where to start for question 4 a) & b)

1 horse -- > 1 head , 4 legs , 1 tail
1 person -- > 1 head , 2 legs

H horses -- > 1 H head , 4 H legs , 1 H tail
P people --> 1 P head , 2 P legs

4 H + 2 P – 1 H – 1 P -- > 62
3 H + 1 P -- > 62

1 H + 1 P – 1 H --> 26
1 P -- > 26

3 H -- > 62 – 26 = 36
1 H -- > 36 ÷ 3 = 12

a) There were 26 people.
b) There were 12 horses.

[firebird]

Dear Vanilla cake and Tang


Many thanks for the solution posted.

With best regards
firebird

[Vanilla Cake]

Tang:

firebird:

4) There were some horses and people on a farm. There were 62 more legs than heads. There were 26 more heads than tails.


a) How many people were there?
b) How many horses were there?

I really do not know where to start for question 4 a) & b)

1 horse -- > 1 head , 4 legs , 1 tail
1 person -- > 1 head , 2 legs

H horses -- > 1 H head , 4 H legs , 1 H tail
P people --> 1 P head , 2 P legs

4 H + 2 P – 1 H – 1 P -- > 62
3 H + 1 P -- > 62

1 H + 1 P – 1 H --> 26
1 P -- > 26

3 H -- > 62 – 26 = 36
1 H -- > 36 ÷ 3 = 12

a) There were 26 people.
b) There were 12 horses.

Hi Tang,
Thks for pointing my mistake for interpreting the question incorrectly. :oops: Sorry to mislead you, firebird. Pls see my workings again:

(a)
There were 26 people
Explanation:
\"There were 26 more heads than tails.\"
-> A horse has a head and a tail , so this does not contribute to the difference.
-> A person has no tail and this contributes to the difference that is 26.

(b)
A horse has 4 legs and a head.
Difference =3
26+62-52=36
36/3=12
Number of horses was 12

This is a 4-mark question from http://www.orlesson.org/orp/09Ma/2009-P6-Math-CA1-PeiHwa.pdf

[starlight1968sg]

Hi,

I need some help.

Jane bought a number of books at an average price of $8. If she decides to buy another book which cost $18, the average price of all the books will become $10. Find the number of books she bought?

It is a p5 Maths question.

MTIA.

Thanks for pointing out my glaring typo error!

[Dharma]

starlight1968sg:

Hi,

I need some help.

Jane bought a number of books at an average price of $18. If she decides to buy another book which cost $18, the average price of all the books will become $10. Find the number of books she bought?

It is a p5 Maths question.

MTIA.

Hi starlight1968sg,

When Jane buys an additional book at $18 which is the average price of the she had bought previously the new average price will still be $18.

Unless the price of the new book is much lower than $18, you will not get a new average price of $10.

Pls check the question.

[firebird]

Dear Vanilla cake


No problem. I really appreciate your help.

Many thanks
firebird

[Dharma]

starlight1968sg:

Hi,

I need some help.

Jane bought a number of books at an average price of $8. If she decides to buy another book which cost $18, the average price of all the books will become $10. Find the number of books she bought?

It is a p5 Maths question.

MTIA.

Thanks for pointing out my glaring typo error!

Total cost of N books = $8N
Total cost of (N+1) books = $10(N+1)

$10(N+1) - $8N = $18
$2N = $18 - $10 = $8
N = 4 (No. of books bought by Jane)