Question

A TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 6 sitcoms and 6 dramas, for a total of 372 minutes of programming, not counting commercials. On Tuesday nights, he has scheduled 2 sitcoms and 6 dramas, for a total of 288 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?

Answer 1

x = length of sitcoms = 21 minutes

y = length of dramas = 42 minutes

Explanation:

Let

x = length of sitcoms

y = length of dramas

6x + 6y = 372 (1)

2x + 6y = 288 (2)

Subtract (2) from (1) to eliminate y

6x - 2x = 372 - 288

4x = 84

x = 84/4

x = 21

Substitute x = 21 into (1)

6x + 6y = 372

6(21) + 6y = 372

126 + 6y = 372

6y = 372 - 126

6y = 246

y = 246/6

y = 41

x = length of sitcoms = 21 minutes

y = length of dramas = 42 minutes