Question

In a recent​ year, companies spent a total of ​$88.8 billion on​ newspaper, television, and radio ads. The total amount spent on television and radio ads was only ​$3.2 billion more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was​ $5.3 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.)

Answer 1

Answer:

The amount spent on radio is $8.5 billion

The amount spent on television is $37.5 billion

The amount spent on newspaper is $42.8 billion

Step-by-step explanation:

Let;

x represent the amount spent on radio ads

y represent the amount spent on television ads

z represent the amount spent on newspaper ads.

The total amount spent on ads

x + y + z = 88.8 ......1

The total amount spent on television and radio ads was only ​$3.2 billion more than the amount spent on newspaper ads alone.

x + y = 3.2 + z

x + y - z = 3.2 .....2

The amount spent on newspaper ads was​ $5.3 billion more than what was spent on television ads.

z = 5.3 + y

z - y = 5.3 ......3

Subtracting equation 2 from equation 1;

(x + y + z) - (x + y - z) = 88.8 -3.2

z + z = 85.6

2z = 85.6

z = 85.6/2

z = 42.8

We can now substitute the value of z into equation 3

42.8 - y = 5.3

y = 42.8 - 5.3

y = 37.5

Substituting y and z to equation 1, we have;

x + 37.5 + 42.8 = 88.8

x =88.8 - (37.5 + 42.8)

x = 8.5

Therefore;

The amount spent on radio is $8.5 billion

The amount spent on television is $37.5 billion

The amount spent on newspaper is $42.8 billion