Tutor MathsGuru: Ask me for your burning Maths questions!

[anonymus]

Dharma:

Almighty:

[quote=\"mathsguru\"]
Hi Almighty,

I don’t really understand what you are trying to say but we know that that the radius of the circle is 14cm and the radius of 14cm is also the side of the small equilateral triangles.

Perimeter of the shaded part
= Length of the 3 sides of a triangle + Curved length of the semicircle
= ( 14 x 3 ) + ( 22/7 x ½ x 14 x 2 )
= 42 + 44
= 86

The perimeter of the shaded part = 86cm

[/quote]Let me put it in a simpler manner.
Pls see the highlighted 14 X 2 in your solution.The straight line of the shaded semicircle is 14 cm. Its the diameter of that semicircle also. Then y do u mulitply by 2? Please see highlighted portion of my solution on top.hope i am clear. Please dharma..dont get irritated..pls explain...

[991narnia]

Pls help me with this question



1. Four children, Eugene, Fann, Grace and Herman, each have some stickers. The number of stickers that Eugene has is 1/2 of the total number of stickers that Fann, Grace, and Herman have. The number of stickers that Fann has is 1/4 of the total number of stickers that Eugene, Grace and Herman have. The number of stickers that Grace has is 2/3 of the total number of stickers that Eugene, Fann, and Herman have. If Herman has 47 stickers, how many stickers should Grace give to Fann so that Eugene and Fann have the same number of stickers?

[Dharma]

anonymus:

Dharma:

[quote=\"Almighty\"]
Let me put it in a simpler manner.
Pls see the highlighted 14 X 2 in your solution.The straight line of the shaded semicircle is 14 cm. Its the diameter of that semicircle also. Then y do u mulitply by 2? Please see highlighted portion of my solution on top.hope i am clear. Please dharma..dont get irritated..pls explain...

[/quote]Hi Almighty and anonymus,

The highlighted in blue “ … 14 x 2” is actually the diameter of a circle.

Diameter of circle = pi x Diameter

The straight lines in the semicircle form equilateral triangles within the circle. Here, if you notice carefully, the sides of the triangles is the length of the radius of the circle and NOT the diameter. I multiplied the radius (14cm) by 2 to get the diameter of the circle.

Now if you notice the highlighted length of the figure above is actually

Total length of 3 equal straight lines + The curved length of the semicircle
= (14cm x 3) + (pi x Diameter x 1/2)
= 42cm + ( 22/7 x 28cm x ½)
= 42cm + 44cm
= 86cm

OR

Based on Almighty’s workings:

If you take the perimeter (highlighted) of 1 sector; you need to find the arc length of the curve with an angle of 60 degrees plus the length of side of the triangle (14cm)

Arc length = 60/360 x pi x Diameter = 1/6 x 22/7 x 2 x 14cm = 44/3cm
Perimeter of the highlighted part of 1 sector = (44/3 + 14)cm
Perimeter of the highlighted part of 3 sectors = (44/3 + 14)cm x 3 = 44cm + 42cm = 86cm

[liketoeat]

Dharma:

liketoeat:

Here's another question.


Each day, Mike saves $0.50 while Carol saves $0.30 more than her. Carol starts saving 6 days after Mike. She has $17.40 more than Mike now. How much does Mike save now? (Ans: $37)

Carol starts saving from Day 6 onwards.
Mike saved $ 3.00 ($0.50/day x 6 days) from Day 1 to Day 5

Day 6 to now; Carol saved $ 20.40 ($17.40 + $3.00) more than Mike.

No. of days from Day 6 to now = $20.40/ ($0.30/day) = 68 days

Amount Mike saved from Day 1 until now = $ 3.00 + ($0.50/day x 68 days) = $37.00

Hi Dharma,

I don't understand why Day 1 to Day 5 is 6 days. Please help me to understand. Thank you.

[Dharma]

liketoeat:

Dharma:

[quote=\"liketoeat\"]Here's another question.


Each day, Mike saves $0.50 while Carol saves $0.30 more than her. Carol starts saving 6 days after Mike. She has $17.40 more than Mike now. How much does Mike save now? (Ans: $37)

Carol starts saving from Day 6 onwards.
Mike saved $ 3.00 ($0.50/day x 6 days) from Day 1 to Day 6

Day 7 to now; Carol saved $ 20.40 ($17.40 + $3.00) more than Mike.

No. of days from Day 7 to now = $20.40/ ($0.30/day) = 68 days

Amount Mike saved from Day 1 until now = $ 3.00 + ($0.50/day x 68 days) = $37.00

Hi Dharma,

I don't understand why Day 1 to Day 5 is 6 days. Please help me to understand. Thank you.[/quote]Should be Day 1 to Day 6. See the amendment in red.

[liketoeat]

Dharma:

liketoeat:

[quote=\"Dharma\"]
Carol starts saving from Day 6 onwards.
Mike saved $ 3.00 ($0.50/day x 6 days) from Day 1 to Day 6

Day 7 to now; Carol saved $ 20.40 ($17.40 + $3.00) more than Mike.

No. of days from Day 7 to now = $20.40/ ($0.30/day) = 68 days

Amount Mike saved from Day 1 until now = $ 3.00 + ($0.50/day x 68 days) = $37.00

Hi Dharma,

I don't understand why Day 1 to Day 5 is 6 days. Please help me to understand. Thank you.

Should be Day 1 to Day 6. See the amendment in red.[/quote]Thank you, Dharma.

[SoWoW]

Hi, i have one question.


Miss Tan wants to give some erasers to her pupils. If she gives each pupil 6 erasers, there will be 3 erasers left. If she gives each pupil 8 erasers, she will be short of 11 erasers. How many erasers does she have?

(Can you also share the concept of such question, thanks so much)

[Brenda10]

SoWoW:

Hi, i have one question.


Miss Tan wants to give some erasers to her pupils. If she gives each pupil 6 erasers, there will be 3 erasers left. If she gives each pupil 8 erasers, she will be short of 11 erasers. How many erasers does she have?

(Can you also share the concept of such question, thanks so much)

It is classifed under \"Gap and Different Concept\"

Working:

8 erasers - 6 erasers = 2 erasers
3 erasers + 11 erasers = 14 erasers
14 / 2 = 7 (Pupils)

7 x 6 + 3 = 45 erasers

Note: We learn the above working from \"Heuristic and Model Approach\" or \"Chanllenging Maths problems made Easy\".

Hope the above useful to you.

[Muffins]

SoWoW:

Hi, i have one question.


Miss Tan wants to give some erasers to her pupils. If she gives each pupil 6 erasers, there will be 3 erasers left. If she gives each pupil 8 erasers, she will be short of 11 erasers. How many erasers does she have?

(Can you also share the concept of such question, thanks so much)

(Called algebraic number equations)

*uses algebraic concepts for normal sums*

6 units + 3 = 8 units - 11

2 units = 14
1 unit = 7
7 X 6 = 42
42 + 3 = 45

[Almighty]

anonymus:

Dharma:

[quote=\"Almighty\"]
Let me put it in a simpler manner.
Pls see the highlighted 14 X 2 in your solution.The straight line of the shaded semicircle is 14 cm. Its the diameter of that semicircle also. Then y do u mulitply by 2? Please see highlighted portion of my solution on top.hope i am clear. Please dharma..dont get irritated..pls explain...

[/quote]Hi dharma,

Very many thanks for yr continuous support...I'm still confused...As anonmus said
Its the diameter of THAT (shaded portion's )semicircle also..right.I understand yr first explanation ie., Perimeter of the shaded part
= Length of the 3 sides of a triangle + Curved length of the semicircle..but y can't i think like this???I treat the shaded portion as a seperate semi circle with its diameter 14 cm. Not the diameter of the big circle...
Anonmus..if u are clear with Dharma's explanation.please clarify to me toooooo...