Please Help Me

Question

A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $45,000 per month.A television ad costs $1000, a radio ad costs $200 , and a newspaper ad costs $500 . The department wants to run 70 ads per month, and have as many television ads as radio and newspaper ads combined. How many of each type of ad can the department run each month?

Answer 1

1. the limit on the total number of advertisements is 70; thus the number of television ads T plus newspaper N plus radio R will equal 70, or T + N + R =70

 

2. they want "as many television ads as radio and newspaper ads combined", thus T = N + R

 

3. since T = N + R, then T + T = 70 or T = 35

 

4. as T = 35 x $1,000, the budget for television ads will be $35,000

 

5. total budget = $45,000 - $35,000 = $10,000 for N and R

 

6. N ads cost $500 each; R ads cost $200 each; let n = number of N ads, and r = number of R ads; then 500n + 200r = $10,000

 

7. n + r = T = 35; then r = 35 - n

 

8. substituting 35 - r into 500n + 200r = $10,000; 500n + 200(35 - n) = 10000; solving, n = 10

 

9. since n = 10, r = 35 - 10 = 25

 

10. 10 N ads @ $500 each = $5,000; 25 R ads @ $200 each = $5,000; total = $10,000

 

thus, 35 T ads @ $1,000 + 25 R ads @ $200 + 10 N ads @ $500 = $45,000 with 70 ads total