Hi Arthur. In order to solve this equation, we should first:
let c represent the number of children that attended the play
let a represent the number of adults that attended the play
We can then set up a system of equations. The first equation would represent the total number of people that attended the play. The second equation would represent the total price of the tickets.
c+a=45
3c+5a=165
We need to isolate one variable in the first equation. If we isolate the c variable, we must move the a variable to the right side of the equation. Doing so yields:
c+a=45
c=45-a (subtraction is the opposite operation of addition)
We now know that the number of children that attended the play is equal to the total number of people that attended the play minus the number of adults that attended the play. We can replace c in the second equation with 45-a , since c=45-a. After that, we can find the number of adults that attended the play.
3a+5c=165
3(45-a) +5a = 165
115-3a +5a = 165 (distributed or multiplied 3 by both terms in the parentheses)
115+2a = 165 (combined like terms, which were -3a and 5a)
2a=50 (subtracted 115 from both sides to isolate 2a)
a=25 (divided by 2 to get a)
We now know that a is equal to 25. Did you remember that c=45-a? we can now find the number of children that attended the play by substituting 25 for a and solving for c.
c=45-a
c=45-25
c=20
To finally answer your question, 25 adults and 20 children attended the play. If you have any questions or want to schedule a lesson with me, feel free to contact me through wyzant.
