SOLUTION: A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $102,400 per month. A television ad

Question 1178145: A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $102,400 per month. A television ad costs $2000, a radio ad costs $100, and a newspaper ad costs $500. The department wants to run 88 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?
television ads
radio ads
newspaper ads
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of tv ads
y = number of radio ads
z = number of news ads

two formulas are indicated.

x + y + z = 88
2000x + 100y + 500z = 102400

they want as many tv ads as radio and news ads combined.
equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 88
2000 * (y + z) + 100 * y + 500 * z = 102400

combine like terms and simplify to get:

2y + 2z = 88
2000y + 2000z + 100y + 500z = 102400

combine like terms again to get:

2y + 2z = 88
2100y + 2500z = 102400

multiply both sides of the first equation by 1050 and leave the second equation as is to get:

2100y + 2100z = 92400
2100y + 2500z = 102400

subtract the first equation from the second to get 400z = 10000

solve for z to get z = 25

since 2y + 2z = 88 and since y = 25, that equation becomes 2y + 50 = 88
subtract 50 from both sides to get 2y = 38
solve for z to get z = 19.

you have y = 19 and z = 25
since x = y + z, then x = 19 + 25 = 44

you have x = 44 and y = 19 and z = 25

go back to your original equations and replace x and y and z with their respective values to get:

x + y + z = 88 becomes 44 + 19 + 25 = 88 which becomes 88 = 88 which is true.
2000x + 100y + 500z = 102400 becomes 2000 * 44 + 100 * 19 + 500 * 25 = 102400 which becomes 102400 = 102400 which is true.

the values of x and y and z are confirmed to be good.

your solution is that 44 television ads and 19 radio ads and 25 news ads can be run each month.

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