SOLUTION: A soap manufacturer decides to spend 60000 rupees on radio, magazine and tv advertising. if he spends as much on tv advertising as on magazines and radio together, and the amount s

Question 1167786: A soap manufacturer decides to spend 60000 rupees on radio, magazine and tv advertising. if he spends as much on tv advertising as on magazines and radio together, and the amount spen on magazines and tv combined equals five times that spent on radio, what is the amount to spent on each type of advertising.using gauss elimination method?
Found 4 solutions by mananth, ikleyn, josgarithmetic, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

A soap manufacturer decides to spend 60000 rupees on radio, magazine and tv advertising. if he spends as much on tv advertising as on magazines and radio together, and the amount spen on magazines and tv combined equals five times that spent on radio, what is the amount to spent on each type of advertising.using gauss elimination method?
A soap manufacturer decides to spend 60000 rupees on radio, magazine and tv advertising.
Let expense on TV be t
Let expense on magazines be m
Let expense on radio be r
t= m+r......................1
m+t = 5r...................2
m+t+r=60000...........3
substitute t in 2
m+t=5r
m+m+r=5r
2m =4r
m=2r
Now m+t=5r
but m=2r
substitute m
2r+t=5r
t=3r
m+t+r=60000...........3
2r+3r+r=60000
6r=60000
r=10000
t=3r
t= 3*10000=30000
m=2r
m=2*10000=20000
you conclude

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
A soap manufacturer decides to spend 60000 rupees on radio, magazine and tv advertising.
if he spends as much on tv advertising as on magazines and radio together,
and the amount spent on magazines and tv combined equals five times that spent on radio,
what is the amount to spent on each type of advertising. using gauss elimination method?
~~~~~~~~~~~~~~~~~~~~~

        It is easy to solve this problem MENTALLY.
        I will show you how to do it. Watch attentively every my step.

(1) Since the soap manufacturer spent as much on tv advertising as on magazines and radio together, we may conclude that he spent exactly half of the 60000 rupees on tv advertising. Thus, he spent exactly 30000 rupees on tv advertising. (2) Next, since the amount spent on magazines and tv combined equals five times that spent on radio, we may conclude that he spent 1/6 of the 60000 rupees, or 10000 rupees, on radio advertising. (3) The rest, 60000 - 30000 - 10000 = 20000 rupees was spent for magazine advertising.

Solved.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

RADIO r MAGAZINE m TV r+m TOTAL 60000

--

"gaussian elimination method?"

2 2 60000 -4 2 0 2 2 60000 4 -2 0 1 1 30000 2 -1 0 ADD these..... 3 0 30000 1 0 10000

This means r=10000
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

It is usually pointless to ask to see a solution using Gauss-Jordan elimination, since there are always an endless number of different paths to the solution using that process.

However, the numbers in this problem are so nice that it can be helpful to solve the problem that way, in order to point out some of the things you can do in general using that process.

So let's do it....

m = amount spent on advertising in magazines
r = amount spent on advertising on radio
t = amount spent of advertising on TV

The given information leads directly to these three equations:

(1) m+r+t = 60000
(2) m+r = t
(3) m+t = 5r

Put these three equations in the required form:

m+r+t = 60000
m+r-t = 0
m-5r+t = 0

And build the initial matrix using those equations:

We first need a "1" in row 1, column 1; we already have that.

Next we need "0"s in the rest of column 1. Since the first column is all "1"s, that is easily accomplished. Replace row 2 with (row 2 minus row 1); replace row 3 with (row 3 minus row 1):

Simplify rows 2 and 3 by dividing by the greatest common factor in each row:

We want "1"s on the main diagonal and "0"s everywhere below the main diagonal; we can do that simply by switching rows 2 and 3:

To finish, we want "0"s above the main diagonal; with this simple example that is easy: replace row 1 with (row 1 minus row 2 minus row 3):

We have the solution.

ANSWER:
m (magazines) 20,000 rupees
r (radio) 10,000 rupees
t (television) 30,000 rupees

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NOTE!...

While this problem lends itself to an easy solution using Gauss-Jordan elimination, it is also very easily solved by standard algebraic methods.

However, the student will get by far the most benefit by working the problem using logical reasoning and simple arithmetic, as demonstrated in the response from tutor @ikleyn.

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