SOLUTION: Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 min, how many comme

Question 152835: Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 min, how many commercials of each type does Rudy play?

Answer by mducky2(62) (Show Source): You can put this solution on YOUR website!
There are two unknowns in this problem: amount of 30-second commercials and amount of 60-second commercials. Any time we need to solve for two unknowns, we always need to set up at least two equations. In order to solve equations, we need to label each type of commercial:
x = amount of 30-second commercials
y = amount of 60-second commercials.

Now let's set up each equation.

We know that there are a total of 12 commercials. Because those commercials are either 30 seconds long or 60 seconds long, we know the sum of both has to equal 12:

There's one equation.

Now for the second equation. We know that the total commercial time is 10 minutes, and we know how long each type of commercial is. To make both units the same, let's convert the commercials' times from seconds to minutes:
30 seconds is .5 minute
60 seconds is 1 minute

The total commercial time should equal the amount of each type of commercial times the length of each type. In other words:

There's the second equation.

Now let's solve the equations. If we solve for one of the variables in the first equation, we can plug it into the second equation.

Plugging back into the second equation:

Now we can use this answer to plug back into the original equation:

Therefore, there are 4 of the 30-second commercials and 8 of the 1-minute commercials.
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