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In a recent year, companies spent a total of $87.5 billion on newspaper, television, and radio ads. The total amount spent on television and
radio ads was only $2.9 billion more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was $5.4 billion
more than what was spent on television ads. How much was spent on each form of advertising? (Hint: Let the variables represent numbers of
billions of dollars.)
How much was spent on newspaper ads? $
How much was spent on television ads? $
How much was spent on radio ads? $ billion
billion
billion

Sagot :

sqdancefan

Answer:

  • newspaper ads: $42.3 billion
  • television ads: $36.9 billion
  • radio ads: $8.3 billion

Step-by-step explanation:

You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.

Setup

Let n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....

  n +t +r = 87.5

  -n +t +r = 2.9

  n -t = 5.4

Solution

The augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.

  • newspaper ads: $42.3 billion
  • television ads: $36.9 billion
  • radio ads: $8.3 billion

__

Additional comment

The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.

View image sqdancefan
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