https://sites.google.com/view/h2mathematicstextbook/home

https://drive.google.com/open?id=0By83v5TWkGjvdGlLd2NkUHBobUk

https://drive.google.com/open?id=0By83v5TWkGjvdGlLd2NkUHBobUk

deon629:

Pls help. TIA.


Charlie had 148 pieces of $2 and $5 notes. She spent 60% of her $5 notes to buy a bag and then her mother gave her another six $2 notes. As a result, the number of $2 notes was thrice as many as the number of $5 notes left. Find the amount of money Charlie had left.

Answer: $308.
Solution:

Let T and F be the initial numbers of $2 and $5 notes. We have

(1) T + F = 148.

After buying the bag, the number of $5 notes she has is 0.4 F.
After her receiving another six $2 notes, the number of $5 notes she has is T + 6.
We are told that she then has thrice as many $2 notes as $5 notes.

Thus,

(2) 3 × 0.4 F = T + 6.

From (1), we have T = 148 - F. Plug this into (2) to get

3 × 0.4 F = 148 - F + 6.

Rearranging, we have 2.2 F = 154, and thus F = 70.

So T = 78.

And so the money she has at the end of the day is

0.4 F × 5 + (T + 6) × 2 = 0.4 × 70 × 5 + (78 + 6) × 2 = 140 + 168 = $308.

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min


If you found this answer helpful, then please help me out by spreading word of my services. I’m a new tutor in Singapore so I need some help getting word out! Thank you!

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ksraja69:

4 men and 4 women are to be seated at round table for dinner.If the men and women take alternate seats, how many arrangements are possible?

Fix any man in place (call him Man #1). To his left is a woman (4 possible choices) --- call her Woman #1. To her left is a man (3 possible choices) --- call him Man #2. To his left is a woman (3 possible choices) --- call her Woman #2. Etc.

Altogether, there are 4 × 3 × 3 × 2 × 2 × 1 × 1 = 144 possible arrangements.

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

http://www.EconsPhDTutor.com

If you found this answer helpful, then please help me out by spreading word of my services. I’m a new tutor in Singapore so I need some help getting word out! Thank you!

dido:

Hi Dr Choo,


Thanks so much for your help. For question 13, the answer in answer sheet is 99.98cm. I think it could be wrong, I am not sure. Nevertheless, we thank you for helping us solve it.

Thanks
Dido

Hi

It was a mistake on my part. As pointed out by speedmaths (thanks!), I incorrectly used the diameter (instead of the radius) to calculate half the circumference of the circle. My answer above has now been corrected.

Best
Dr. Choo

dido:

Hi,


I am trying to help my P6 child in his Math revision, but I couldn't solve. Can someone help? Thanks a million.

http://i67.tinypic.com/e71768.jpg\">

God Bless

13. I interpret this question to be asking for the length of the perimeter of Figure 1 with which Ball A comes into contact, during its journey.

This length is highlighted in red, green, and blue colours in the figure below.

The red lengths on the left and right sides simply add up to 2 × 15 cm = 30 cm.

The green length on the upper side is 38 cm - 2 × 7 cm = 24 cm. The blue length on the upper side is half the circumference of the circle: π̶r̶=̶ ̶3̶.̶1̶4̶ ̶×̶ ̶7̶ ̶=̶ ̶2̶1̶.̶9̶8̶ I made a mistake here previously of using the diameter instead of the radius. Now corrected: πr= 3.14 × 7 × 0.5 = 10.99.

Altogether, the green and blue lengths on the upper side add up to 34.99 cm.

Symmetrically, the green and blue lengths on the lower side add up to 34.99 cm.

Altogether then, the total length is 30 + 34.99 + 34.99 = 99.98 cm.

http://i68.tinypic.com/vp9ndk.jpg\">

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

http://www.EconsPhDTutor.com

If you found this answer helpful, then please help me out by spreading word of my services. I’m a new tutor in Singapore so I need some help getting word out! Thank you!

dido:

Hi,


I am trying to help my P6 child in his Math revision, but I couldn't solve. Can someone help? Thanks a million.

http://i66.tinypic.com/2drcr4z.jpg\">

God Bless

15(a) 14 cm × 756.25 cm² =10,587.5 cm³.

15(b) Let X be the water level of Tank B after all the pouring is done.

Then (X - 20) cm is the increase in the water level of Tank B and (28 - X) cm is the decrease in the water level of Tank A.

If the water level in Tank A falls by 1 cm, then its volume decreases by 1 cm × 756.25 cm² = 756.25 cm³.

If the water level in Tank B rises by 1 cm, then its volume increases by 1 cm × 5 cm × 5 cm = 25 cm³.

We know moreover that the increase in volume of water in Tank B equals the decrease in volume of water in Tank A. Therefore:

(X - 20) × 25 = (28 - X) × 756.25.

Do the algebra:

⇒ (25 + 756.25) X = 28 × 756.25 + 20 × 25

⇒ 781.25X = 21675

⇒ X = 27.744.

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

http://www.EconsPhDTutor.com

If you found this answer helpful, then please help me out by spreading word of my services. I’m a new tutor in Singapore so I need some help getting word out! Thank you!