Solve the problem using the elimination method.
-There were 380 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $600. How many adults and how many children attended?
A)150 adults and 230 children
B)80 adults and 300 children
C)160 adults and 220 children
D)220 adults and 160 children

Question

Quizplus · Accepted Answer

To solve this problem using the elimination method, we set up two equations based on the information given. Let $A$ represent the number of adults and $C$ represent the number of children. We have:1. $A + C = 380$ (since there were 380 people at the play)2. $2A + 1C = 600$ (since the admission receipts were $600, with adults paying $2 and children $1)To use the elimination method, we can multiply the first equation by -1 to make it easier to eliminate one of the variables when we add the two equations together. This gives us:- $A + C = 380$ becomes $-A - C = -380$Adding this to the second equation:- $(-A - C) + (2A + C) = -380 + 600$- $A = 220$Substituting $A = 220$ into the first equation:- $220 + C = 380$- $C = 160$Therefore, there were 220 adults and 160 children at the play.

Solve the Problem Using the Elimination Method