A local dinner theater sells adult tickets for $105 each and children’s tickets for $60 each. For a certain show the theater sells 84 tickets for a total of $7155. Write a system of equations that models this problem and then show all the steps to solve your system of equations using linear combination.
+122 Since know the number of tickets is 84, the number of children's tickets can expressed as the total number of tickets minus the adult tickets or 84-x where x is the number of adult tickets. Then we have the following equation:
105*x+60(84-x)=7155
Factor out the equation to get
105x+60*84-60x=7155
Next up we get x alone on the left side of the equation and get
105x-60x=7155-60*84
45x=7155-5040
45x=2115
x=2115/45
x=47
y=84-47
y=37
You can check this by putting the values into the equation: 47*105+60*37
Cheers
