Question

a radio plays 16 commercials in an hour. a commercial is either 30 - seconds long or 60 - seconds long. the total commercial time is 13 minutes. if x represents a 30 - second commercial and y is a 60 - second commercial, which equations would you enter into a graphing calculator to find how many of each type of commercial is played? check all that apply.\\(\square\\ x + y = 13\\)\\(\square\\ x + y = 16\\)\\(\square\\ 0.5x + y = 13\\)\\(\square\\ 0.5x + y = 16\\)\\(\square\\ 0.5x + y = 29\\)

Explanation:

Step1: Analyze the number of commercials

The total number of commercials is 16, and \(x\) is the number of 30 - second commercials, \(y\) is the number of 60 - second commercials. So the equation for the number of commercials is \(x + y=16\).

Step2: Analyze the total time of commercials

Since 30 seconds \( = 0.5\) minutes and 60 seconds \( = 1\) minute. The total commercial time is 13 minutes. The time from 30 - second commercials is \(0.5x\) minutes and from 60 - second commercials is \(y\) minutes. So the equation for the total time is \(0.5x + y=13\).

Answer:

B. \(x + y = 16\)
C. \(0.5x + y = 13\)