how do you set up this equation

Question

X-files, Will and Grace, and Seinfeld are three of the most popular television shows of all time. The total number of episodes of these three show is 575. There are 21 more episodes of x-files than Seinfeld, and the difference between the number of episodes of Will and Grace and Seinfeld is 14. Find the number of episodes of each show. 

 

I have an idea of how to set this equation. Can someone tell me if I'm on the right track?

let x-files be=x

Will and Grace=w

Seinfeld=s

x+w+s=575

s=x+21

w-s=14

 

I know the answers already but I feel like something is missing in the equations. I think I can also write equation 2 as s-21=x but I'm still having trouble actually solving this problem with the equations I have. The answer to this problem is x-files=201

Will and Grace=194

Seinfeld=180

Answer 1

To solve these equations you must use substitution to find one solution:

Plus your equation 2 is wrong it should be x=s+21

Since each equation has two or more unknowns you must derive an equation with one.

so:

 

x+w+s=575  and x=s+21

(s+21)+w+s=575 and w-s=14 so w=s+14 and 

(s+21)+(s+14)+s=575

3s = 575-21-14

s=180

w=s+14 = 180+14 = 194

x=s+21 = 180+21 = 201

 

 

 

 

Answer 2

Use the given information to set up a solution in terms of only one variable. 

 

s = number of Seinfeld

s + 21 = number of X-Files

s + 14 = number of Will and Grace

 

s + (s + 21) + (s + 14) = 575

 

3s + 35 = 575

 

Seinfeld:  s = (575 - 35)/3 = 180

X-Files:  s + 21 = 180 + 21 = 201

Will and Grace:  s + 14 = 180 + 14 = 194