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. X y = 13 x y = 16 0. 5x y = 13 0. 5x y = 16 0. 5x y = 29.

Answer 1

The equations that should be entered into a graphing calculator to find how many of each type of commercial is played are: 0.5x + y = 13 and x + y = 16.

Step-by-step explanation:

Let x represent the number of 30-second commercials and y represent the number of 60-second commercials. The total commercial time of 13 minutes (or 780 seconds) translates to 0.5x + y = 13, considering that each 30-second commercial contributes 0.5x to the total time.

Additionally, the total number of commercials played in an hour is 16, leading to the equation x + y = 16, as the sum of both types of commercials equals the total count of 16 commercials.

These equations can be solved simultaneously using a graphing calculator by plotting the two equations on the same graph to find the intersection point, which represents the values of x and y, i.e., the number of 30-second and 60-second commercials played, respectively.

Understanding how to set up and solve equations based on given conditions is crucial for solving problems involving unknown quantities, allowing for effective use of mathematical tools like graphing calculators.

Answer 2

The correct equations to enter into a graphing calculator are: b. x + y = 16 and c. 0.5x + y = 13

Equation b (x + y = 16) represents the total number of commercials played, which is 16. It ensures that the sum of 30-second commercials (x) and 60-second commercials (y) equals 16.

Equation c (0.5x + y = 13) accounts for the total commercial time. It converts the 30-second commercials (x) into minutes by multiplying them by 0.5, and then adds them to the 60-second commercials (y) to ensure the total equals 13 minutes.

The other options are not accurate for the following reasons:

a. x + y = 13 only accounts for the number of commercials, not their total time.

d. 0.5x + y = 16 incorrectly equates the total time to 16 minutes, when it should be 13 minutes.

e. 0.5x + y = 29 is not a valid equation in this context, as it doesn't correspond to any of the given information.