Math Is Fun Forum

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Please Help Answer These

Hi;

Please I need some help answering these. I want to be sure I'm on the right track. Thanks in advance.

#1.   The population of a town increases by 20 percent every year. The Local Government grants the town $15.00 per head at the beginning of every year. If the population of the town was 3000 in the year 2003, calculate the Government's total grant to the town from 2003 to 2007.

#2.  A trader bought some bags of rice and some bags of beans for sale in his shop. Each bag of rice costs ₩2250.00 while each bag of beans costs  ₩2400.00. If the trader bought 17 bags altogether and paid  ₩39600.00, how many  bags of beans did he buy? (Please for this, I did guess work and had 9 as the answer. However I need to show working.)
#3.

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math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Please Help Answer These

#3.   A garden in the form of a square is surrounded by a path which is 1 m wide om two opposite sides and 1/2 m wide on the other two opposite sides. If the area of the path is 17 m^2, calculate the:
(a) perimeter of the garden
(b) area of the space covered by the garden and the path.

Thank you in advance.

math9maniac.

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phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Please Help Answer These

Hi math9maniac;

#3.

(a) perimeter of the garden = 4x
(b) area of the space covered by the garden and the path = AB(x+1)m²

I haven't completed it, but you can probably finish it from here...

Last edited by phrontister (2017-02-26 23:42:14)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Please Help Answer These

hi math9maniac

#1.   The population of a town increases by 20 percent every year. The Local Government grants the town $15.00 per head at the beginning of every year. If the population of the town was 3000 in the year 2003, calculate the Government's total grant to the town from 2003 to 2007.

That's not too many years to calculate it year by year:

20% increase means the new pop is 120% of what it was; so multiply the old value by 1.2

beginning of year

2003:   3000 x 15
2004    3000 x 1.2 x 15
2005    3000 x 1.2^2 x 15
....................................

If it was a lot more years you could use the formula for geometric progressions

http://www.mathsisfun.com/algebra/seque … etric.html

3000 and 15 are common factors, which leaves a GP with a first term of 1 and a ratio of 1.2.  n=5

A trader bought some bags of rice and some bags of beans for sale in his shop. Each bag of rice costs ₩2250.00 while each bag of beans costs  ₩2400.00. If the trader bought 17 bags altogether and paid  ₩39600.00

Introduce two variables, R and B for the number of bags of rice and beans respectively.  Form two equations using the given information:

Solve using simultaneous equation techniques.
http://www.mathsisfun.com/algebra/syste … tions.html

Bob

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Sometimes I deliberately make mistakes, just to test you!  …………….Bob

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Please Help Answer These

Hi Bob and phrontister;

I am grateful for your responses. I'll proceed with your methods and let you know how I do with the rest.

math9maniac.

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Only a friend tells you your face is dirty.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Please Help Answer These

Hi Bob and phrontister;

I have succeeded in solving #2. The problem was getting the second equation but thanks for opening my eyes. Only I have difficulty with #3. I guess I need further explanation and assistance.

Thanks.

math9maniac.

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phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Please Help Answer These

Hi math9maniac;

In my drawing I set one side of the garden, FG, as being x metres long. The garden is a square, and so each of the other three sides is also x metres long.

Knowing that two opposite sides of the surrounding path are ½ a metre wide enables us to calculate BC's length as x + ½ + ½ = x + 1, which because of symmetry is also AD's length. Similarly, you can calculate the lengths of AB and DC in terms of x.

That gives us enough information to obtain the area of the path, given as 17m², in terms of x.

Then solve for x, and from there you can answer questions (a) and (b).

Btw, the 'area of the space covered by the garden and the path' in question (b) is simply the area of the space within outer bounds ABCD of the path.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Please Help Answer These

Thanks so much phrontister. I'm grateful. I'm gonna try it again.  Will post my answers for approval. Thanks.

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math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Please Help Answer These

Hi;

Here is what I have as answersfor #3.

(a)  20 m
(b)  42 m^2

Is that correct? Thanks.

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phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Please Help Answer These

Yes, those two answers are correct.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Please Help Answer These

Thanks so much. Love you bunches.

I love MIF.

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