Tutor MathsGuru: Ask me for your burning Maths questions!

[Superbugs]

CoffeeCat:

Superbugs:

Hi there, appreciate it that someone can assist me on the following questions:


Q1) There are 8 stacks of chairs and 12 chairs in each stack. Each chair is equally spaced apart to form the perimeter of a rectangle. If the no. of chairs placed along its length is thrice the no. of chairs placed along its breadth, how many chairs are placed equally along one of the length of the rectangle.

12x9 = 108
108-4 (4 corners) = 104
108/8 = 13
13x3=39
39+2 (2 corners) = 41

But the answer is 42 and instead of minusing the 4 corners, they add the 4 corners
108+4=112
112/8=42
Why is that so?

Q2) J bought some strawberries and wanted to put them in boxes. If she put 4 strawberries into each box, there would be 3 strawberries left. If she put 6 strawberries into eah box, she would have 5 strawberries left.

If the no. of strawberries was between 100 and 150, how many strawberries did J buy?

I used the common multiple method but got many answers:

Common Multiple of 4, starting with 100 plus 3 excess:
103, 107, 111, 114, 119, 123, 127, 131, 135 etc

Common Multiple of 6, starting with 102 plus 5 excess:
107, 113, 119, 125, 131, 137

Why the answer is not 107 or 119 but 131? If this is not the correct method to apply, any other method?

Qns 1)
\"If the no. of chairs placed along its length is thrice the no. of chairs placed along its breadth\".
The 4 corners....the 4 chairs are only counted once. So you have to add 4 so that you really get the total no. of chairs for length + breadth. If you minus the 4, then the above sentence is no longer true.
Qns 2)
Maybe there is a typo with the question. Your method is correct. Although the fastest direct method is to notice that any number which is 1 less than a multiple of 12 will satisfies the 2 conditions.
(let the ans be x. Notice x+1 will be a common multiple of 4 and 6, implying x+1 must be a multiple of 12)

Hi Coffeecat,

Tks for your prompt reply but why add 4 where the total no. of chairs is only 108? This is something which I do not understand.

The sec question was correctly listed but ans is only 131...

[CoffeeCat]

Superbugs:

Hi Coffeecat,

Tks for your prompt reply but why add 4 where the total no. of chairs is only 108? This is something which I do not understand.

The sec question was correctly listed but ans is only 131...

Ar, this is a bit hard to explain.
Why do u choose to minus 4?
From your working, I think u kinda understand what u r supposed to do.
To find the total number of chairs along the length + total number of chairs along the breadth
Minus-ing the 4 corners isnt going to be correct.... We add the four corners because ...

maybe you wana draw a diagram
X X X X X X X X X
X X
X X X X X X X X X
(please imagine the 2nd X in the 2nd row as to the far right...)
In this diagram, there are 9 X along the length, 3 along the breadth.
What's the total?
7 + 7 + 1 + 1 + 4 (corners) = 20
But length = 9 breadth =3.
2 length + 2 breadth = 24
There is a shortage of 4 because the 4 corners are only counted once in the first scenario when they are in fact double counted in the second scenario.

[Dharma]

Superbugs:

Dharma:

Total No. of Ducks = D

Total No. of Cows = C
Total no. of legs = 2D + 4C

Ratio of the no. of legs of ducks : no. of legs of cows = 2D : 4C = 5 : 9
18D = 20C
D : C = 20 : 18

Total no. of ducks and cows = 20 + 18 = 38

How did you derive at 18D:20C? You mean cross multiply 2D with 9 and 4C with 5? If yes, why?

You can use fractions instead of ratios.
2D/4C = 5/9
Cross multiply to get
18D = 20C

D/C = 20/18 => Ratio of D : C = 20 : 18

[2cutis]

Please help :imdrowning: ,


We know 2 sq is 2x 2 and 2 cube is 2x2x2 but what's the solution
to 2 to the power of 50?

[MathIzzzFun]

2cutis:

Please help :imdrowning: ,


We know 2 sq is 2x 2 and 2 cube is 2x2x2 but what's the solution
to 2 to the power of 50?

Hi

2 to power of 50
= 2 x 2 x 2 x 2 x ... x2 x 2
(50 '2's)
= 1024 x 1024 x 1024 x 1024 x 1024
= 1 petabyte

cheers.

[Dharma]

CoffeeCat:

Superbugs:

Hi Coffeecat,

Tks for your prompt reply but why add 4 where the total no. of chairs is only 108? This is something which I do not understand.

The sec question was correctly listed but ans is only 131...

Ar, this is a bit hard to explain.
Why do u choose to minus 4?
From your working, I think u kinda understand what u r supposed to do.
To find the total number of chairs along the length + total number of chairs along the breadth
Minus-ing the 4 corners isnt going to be correct.... We add the four corners because ...

maybe you wana draw a diagram
X X X X X X X X X
X X
X X X X X X X X X
(please imagine the 2nd X in the 2nd row as to the far right...)
In this diagram, there are 9 X along the length, 3 along the breadth.
What's the total?
7 + 7 + 1 + 1 + 4 (corners) = 20
But length = 9 breadth =3.
2 length + 2 breadth = 24
There is a shortage of 4 because the 4 corners are only counted once in the first scenario when they are in fact double counted in the second scenario.

Hi Superbugs,

Think there is a typo error in the Qn ... should be 9 stacks of chairs instead of 8.
Total number of chairs = 12 x 9 = 108
Number of chairs in the corners = 4
Balance number of chairs to be placed at equal spacing between the corners = 108 – 4 = 104
L + B = 104/2 = 52
(L + 2)/ (B + 2) = 3/1
L + 2 = 3B + 6
L – 3B = 4
4B = 48
B = 12
L = 52 – 12 = 40
Number of chairs placed along one of the length = 40 + 2 = 42

[Superbugs]

Dharma:

CoffeeCat:

[quote=\"Superbugs\"]

Hi Coffeecat,

Tks for your prompt reply but why add 4 where the total no. of chairs is only 108? This is something which I do not understand.

The sec question was correctly listed but ans is only 131...

Ar, this is a bit hard to explain.
Why do u choose to minus 4?
From your working, I think u kinda understand what u r supposed to do.
To find the total number of chairs along the length + total number of chairs along the breadth
Minus-ing the 4 corners isnt going to be correct.... We add the four corners because ...

maybe you wana draw a diagram
X X X X X X X X X
X X
X X X X X X X X X
(please imagine the 2nd X in the 2nd row as to the far right...)
In this diagram, there are 9 X along the length, 3 along the breadth.
What's the total?
7 + 7 + 1 + 1 + 4 (corners) = 20
But length = 9 breadth =3.
2 length + 2 breadth = 24
There is a shortage of 4 because the 4 corners are only counted once in the first scenario when they are in fact double counted in the second scenario.

Hi Superbugs,

Think there is a typo error in the Qn ... should be 9 stacks of chairs instead of 8.
Total number of chairs = 12 x 9 = 108
Number of chairs in the corners = 4
Balance number of chairs to be placed at equal spacing between the corners = 108 – 4 = 104
L + B = 104/2 = 52
(L + 2)/ (B + 2) = 3/1
L + 2 = 3B + 6
L – 3B = 4
4B = 48
B = 12
L = 52 – 12 = 40
Number of chairs placed along one of the length = 40 + 2 = 42[/quote]Tks for the explanation. The latter might be too difficult for my DD to understand.

I have another question, appreciate your help:

Jovi has 2 strings, string A and string B. Initially, string A was thrice the length of string B. Jovi then cut 9.1m from string A and 140cm from string B. The length of string B became 1.5 times of string A. What is the length of string A at first? Express your answer in cm?

[MathIzzzFun]

Superbugs:

I have another question, appreciate your help:

Jovi has 2 strings, string A and string B. Initially, string A was thrice the length of string B. Jovi then cut 9.1m from string A and 140cm from string B. The length of string B became 1.5 times of string A. What is the length of string A at first? Express your answer in cm?

Hi

Hope this helps :lol:

http://www.flickr.com/photos/62167097@N02/5709910478/in/photostream

cheers.

[2cutis]

MathIzzzFun:

2cutis:

Please help :imdrowning: ,


We know 2 sq is 2x 2 and 2 cube is 2x2x2 but what's the solution
to 2 to the power of 50?

Hi

2 to power of 50
= 2 x 2 x 2 x 2 x ... x2 x 2
(50 '2's)
= 1024 x 1024 x 1024 x 1024 x 1024
= 1 petabyte

cheers.

Thanks, MathIzzzFun

[MathIzzzFun]

2cutis:

MathIzzzFun:

[quote=\"2cutis\"]Please help :imdrowning: ,


We know 2 sq is 2x 2 and 2 cube is 2x2x2 but what's the solution
to 2 to the power of 50?

Hi

2 to power of 50
= 2 x 2 x 2 x 2 x ... x2 x 2
(50 '2's)
= 1024 x 1024 x 1024 x 1024 x 1024
= 1 petabyte

cheers.

Thanks, MathIzzzFun[/quote]you are welcome :lol:

cheers.