Tutor MathsGuru: Ask me for your burning Maths questions!

[Almighty]

Hi,


Can anyone help me to solve this problem?

What is the maximum number of right angled triangles, of base 5 cm and height 6 cm, that can be cut from a rectanglular sheet of paper, 49cm long and 34 cm wide?
Ans : 48

[CoffeeCat]

Almighty:

Hi,


Can anyone help me to solve this problem?

What is the maximum number of right angled triangles, of base 5 cm and height 6 cm, that can be cut from a rectanglular sheet of paper, 49cm long and 34 cm wide?
Ans : 48

49/5 = 9 r 4. 49/6 = 8 r 1
34/5 = 6 r 4. 34/6 = 5 r 4

intuitively you want to minimise wastage so you should choose to cut the triangles with theheight 6 cm along the 49 cm long side, ie 8 times 6 = 48

[Vanilla Cake]

abc_parent:

Ali, Bala and Charles shared a tin of cookies. Ali took 5/6 of the tin of cookies and 1/3 of a cookie. Bala took 5/6 of the remaining tin of cookies and 1/3 of a cookie. Charles received only 2 cookies. How many more cookies did Ali have than Bala?

This question was first posted by OK Lor on 12 Apr 2010 08:43 and solved by http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=6373&postdays=0&postorder=asc&start=790 on 12 Apr 2010 09:02 and http://www.postimage.org/image.php?v=gxxlNRS on 12 Apr 2010 13:12

[Vanilla Cake]

abc_parent:

Lily, Mina and Oscar each donated some money to charity. The donation made by Lily was 2/3 as much as the total amount donate by Mina and Oscar. Mina donated 1/5 as much as the total donated by Lily and Oscar. If Oscar donated $360 more than Mina, how much did Lily donate?

Donation made by Lily = 2/5 of the total donation
Donation made by Mina = 1/6 of the total donation
Donation made by Oscar = 1-2/5-1/6 = 13/30 of the total donation

13/30-1/6 = 8/30
8/30 -> $360
Lily : 2/5 = 12/30
12/30 -> 360/8x12 = 540

Amount of donation made by Lily = $540

OR

L : M+O
2 : 3
12 : 18

M : L+O
1 : 5
5 : 25

Lily = 12 units
Mina = 5 units
Oscar = 13 units

(13-5) units = 8 units
8 units = 360
12 units = 540

Amount of donation made by Lily = $540

[Sun_2010]

Almighty:

Hi,


Can anyone help me to solve this problem?

What is the maximum number of right angled triangles, of base 5 cm and height 6 cm, that can be cut from a rectanglular sheet of paper, 49cm long and 34 cm wide?
Ans : 48

Is the answer 48?
Firstly it should be 48x2 since it is right angled triangles not rectangles.

But even with rectangles, it will be 52

Explanation:
The rectangle 34 x 49 = (24+10) x (30+19)
= 24x30 + 10x49 + 24x19
This can be visualised as take out a 24x30 rectangle from the given 30x49 rectangle.
That leaves u with an L shaped piece which can be represented by 2 rectangles 10x49 and 24x19


So 24x30 will have (24/6) x (30/5) = 4x6=24 rectangles
and 10x49 will have (10/5) x (49/6) = 2x8=16 rectangles
(reminder of 1x10 wasted)
and 24 x 19 will have (24/6) x (19/5) = 4x3=12 rectangles
(reminder of 4x24 wasted)

Hence total rectangles = 24+16+12 = 52
So total triangles = 52 x 2 = 104

Hope that is not confusing.
Dunno how to upload the diagram, that would have been clearer.

[Almighty]

CoffeeCat:

Almighty:

Hi,


Can anyone help me to solve this problem?

What is the maximum number of right angled triangles, of base 5 cm and height 6 cm, that can be cut from a rectanglular sheet of paper, 49cm long and 34 cm wide?
Ans : 48

49/5 = 9 r 4. 49/6 = 8 r 1
34/5 = 6 r 4. 34/6 = 5 r 4

intuitively you want to minimise wastage so you should choose to cut the triangles with theheight 6 cm along the 49 cm long side, ie 8 times 6 = 48

Thankyou very much for the detailed quickest reply coffeecat

[Almighty]

Hi,


Please help to solve this problem.

Ken took 20 minutes to cycle from point X to Y. On his return journey he took only 12 minutes when he cycled 6 km/hr faster. What was the distance between point X and Point Y ?

Ans : 3 Km

[corneyAmber]

Almighty:

Hi,


Please help to solve this problem.

Ken took 20 minutes to cycle from point X to Y. On his return journey he took only 12 minutes when he cycled 6 km/hr faster. What was the distance between point X and Point Y ?

Ans : 3 Km

Let d be the distance between X and Y.
Let s be the speed at first.

distance = speed x time

Travelling from X to Y,
20 mins = 1/3h
d = 1/3s
On return journey Y to X, d = (s+6)*1/5

XY=YX (distance)
1/3s = (s+6)*1/5
1/3s = 1/5s + 6/5
(5-3)/15s = 6/5
2/15 s = 6/5
s = 6/5 * 15/2 = 9km/h

Hence d = 1/3s = 1/3 * 9 = 3km

[Vanilla Cake]

Almighty:

Ken took 20 minutes to cycle from point X to Y. On his return journey he took only 12 minutes when he cycled 6 km/hr faster. What was the distance between point X and Point Y ?

Constant distance

20 min = 1/3 of an hour
12 min = 1/5 of an hour

Ratio of time
1/3 : 1/5
5 : 3

Ratio of speed
3 : 5

Difference = (5-3) units = 2 units
2 units = 6 km/h
1 unit = 3 km/h

Distance between point X and point Y = 3x3x1/3= 3 km.

[CoffeeCat]

Almighty:

CoffeeCat:

[quote=\"Almighty\"]Hi,


Can anyone help me to solve this problem?

What is the maximum number of right angled triangles, of base 5 cm and height 6 cm, that can be cut from a rectanglular sheet of paper, 49cm long and 34 cm wide?
Ans : 48

49/5 = 9 r 4. 49/6 = 8 r 1
34/5 = 6 r 4. 34/6 = 5 r 4

intuitively you want to minimise wastage so you should choose to cut the triangles with theheight 6 cm along the 49 cm long side, ie 8 times 6 = 48

Thankyou very much for the detailed quickest reply coffeecat[/quote]Actually Almight you might wana double check the given answer because as sun_2010 pointed out there are 2 mistakes in my working.