math question! super confused

Question

A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $49,100 per month. A television ad costs $1000, a radio ad costs $100, and a newspaper ad costs $500. The department wants to run 74 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

This boils down to 3 equations and 3 unknowns. We are assuming the company plans to use all $49,100 of its advertising budget.

Let T = # television ads, R = #radio ads, N = #newspaper ads

Then T + R + N = 74 (number of ads)

T = R + N (TV ads equal number of radio and newspapers combined)

And finally, the cost of the ads:

1000T + 100R + 500N = 49100.

There are multiple ways to solve this system. Probably easiest is to replace T with R + N in the first equation, and solve for N. (N=37-R).

Now you can rewrite the 3rd (cost) equation in terms of R, replacing T with R + N and N with 37 - R. Solve for R, then N, then T.