How many of each type of ad can the department run each month?

Question

A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $49,500 per month. A television ad costs $1000, a radio ad costs $100, and a newspaper ad costs $400. The department wants to run 78 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

t = r+n

t+r+n= 78

1000t+100r + 400n= 49500

3 equations 3 unknowns

solve by substitution, elimination or matrix algebra

r+n+r+n= 78

r+n = 78/2 = 39

r= 39-n

t= 78-39 = 39

1000(39) + 100(39-n) +400n = 49500

400n -100n = 49500-39000-3900

300n = 6600

n = 66/3 =22 newspaper ads

r = 39-22 = 17 radio ads

t = 34+5 = 39 TV ads