Tutor MathsGuru: Ask me for your burning Maths questions!

[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)

[starlight1968sg]

Dharma:

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)

yes, the ans is 4. Without the use of equation method, how can we solve it using model? I have been trying this p5 question for days!
MTIA.

[CoffeeCat]

The average price is $8 . The extra value that causes the increase in average price across all books (including the new book) is $18-$10=$8.

since this extra$10 increases theaverage prices of all books by $2, there are 10/2=5 books.(including the new book).

[Vanilla Cake]

starlight1968sg:

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.

Hi starlight1968sg,
For info and there is a helpful http://psle2010a.blogspot.com/2010/03/mathsp5averagea001.html that provides solutions for Maths questions. Your question has been selected and two different methods without using algebra have been used to solve it.