Variable equation

Question

Movie tickets to a nighttime movie cost $8 and a daytime movie costs $3. Susan goes to the movie a total of 7 times and spends $41.   Define two variables x and y explaining the meaning of each and two equations that represent this scenario

Answer 1

let X are nighttimes, Y are daytimes

 

solution:

8X+3Y=41

X+Y=7

 

and then

(one way)

8X+3Y=41
3X+3Y=21 ,    8X+3Y-(3X+3Y)=41-21  ,  5X=20, X=4, Y=7-X, Y=7-4=3

 

(the other way)

8X+3Y=41
8X+8Y=56,    8X+8Y-(8X+3Y)=56-41,  5Y=15, Y=3, X=7-Y, X=7-3=4

 

So Susan go to nighttime movie 4 times, and go to daytime movie 3 times.