First we are going to set up two equations:
1) [tex] x+y=168 [/tex]
2) [tex] y=3x [/tex]
where x is the number of hotdogs sold, and y is the number of sodas sold. Let's subtract x from the second equation and set equal to 0:
1) [tex] x+y=168 [/tex]
2) [tex] 3x-y=0 [/tex]
Then let's add the two equations together to cancel out the y variable:
[tex] x+y=168 [/tex]
+ [tex] 3x-y=0 [/tex]
---------------------------------
[tex] 4x=168 [/tex]
Then solve for x:
[tex] x=42 [/tex]
So then return to equation 1 and plug in x to solve for y:
[tex] x+y=168 [/tex]
[tex] 42+y=168 [/tex]
[tex] y=126 [/tex]
So then we know that x = 42 and y = 126; therefore, there were 42 hotdogs sold, and there were 126 sodas sold.
