SOLUTION: Please help me in this question: A soap manufacturer decides to spend 600,000 rupees on radio, magazine and TV advertising. If he spends as much on TV advertising as on magazine

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Question 1165817: Please help me in this question: A soap manufacturer decides to spend 600,000 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 equal five times that spent on radio, what is the amount
to be spent on each type of advertising? Solve by Gauss-Elimination method.
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
R = rupees spent on radio
M = rupees spent on magazine
T = rupees spent on television advertising

R + M + T = 600000
T = M + R
M + T = 5R

Solve the system of equations to get (R, M, T) = (100000, 200000, 300000)
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let T = spending on TV;  R = spending on radio and M = spending on magazines.


From the condition, we have


    T + (R + M) = 600000

    T - (R + M) = 0.


It immediately implies that  


    T = R + M = 600000/2 = 300000.     (1)


In addition, from the condition, we are given that 

    T + M = 5R,    or

    300000 + M = 5R,    or

    5R - M = 300000.     (2)


So, from (1) and (2) we have


    R  + M = 300000,      (3)

    5R - M = 300000.      (4)


Add equations (3) and (4).  You will get

    6R     = 600000,

     R     = 600000/6 = 100000.


ANSWER.  R = 100000  (radio);  T = 300000 (TV)  and  M = 200000 (magazines).

Solved.



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