High school algebra

Question

A TV station executive is planning the new lineup for next season’ shows. On Monday nights, there will be 4 sitcoms and 2 dramas, including everyone favorite drama “Teen Wolf”, for a total of 172 minutes of programming, not counting commercials. On Tuesday nights, 5 sitcoms and 4 dramas, including everyone’s favorite sitcom, “The Big Bang Theory”, for a total of 272 minutes of non-commercial programming has been scheduled. All sitcoms have the same length and all dramas have the same length.

Write equations that represent the length of each type of show. How long is each type of show?

Answer 1

Let x = the length in minutes of sitcoms

Let y = the length in minutes of dramas

The equations are:

4x+2y=172

5x+4y=272

You can solve this using the addition method. First step is multiply the first equation by -2.

-2(4x+2y=172) = -8x-4y=-344

-8x-4y=-344

5x+4y=272 Second equation was not changed. Next step is add the 2 equations together. Since the y term has the same coefficient and the signs are opposite, this term cancels out.

-3x=-72 Divide both sides by- 3

-3x/-3=-72/-3

x=24

To find y you can substitute x into either original equation. I will use the first one.

4x+2y=172

4(24)+2y=172

96+2y=172 Subtract 96 from both sides

96-96+2y=172-96

2y=76 Divide both sides by 2

2y/2=76/2

y=38

There are 24 minute sitcoms and 38 minute dramas