Question 258311
Movie tickets cost $25 for adults, and $5.00 for children. Last night a total of 305 tickets were sold totalling $6025, How many of each ticket was sold? 


let a = number of adult tickets sold.
let c = number of child tickets sold.


25 * a + 5 * c = 6025


a + c = 305


you have 2 equations that have to be solved simultaneously (same solution for both equations).


solve for a or c in the second equation and then use that to solve for the remaining variable in the first equation.


a + c = 305


solve for a to get:


a = 305 - c


substitute for a in the first equation.


first equation is:


25 * a + 5 * c = 6025


substitute 305 - c for a to get:


25 * (305 - c) + 5 * c = 6025


simplify to get:


7625 - 20*c = 6025


subtract 7625 from both sides of the equation to get:


-20*c = 6025 - 7625 = -1600


divide both sides of the equation by -20 to get:


c = -1600/-20 = 80


since a + c = 305, then a must be equal to 305 - 80 = 225


225 + 80 = 305


25 * 225 + 80 * 5 = 5625 + 400 = 6025


numbers look good.


answer is:


number of adult tickets is 225
number of child tickets is 80


the number of tickets sold is a + c = 305


the amount of money made is 25*a + 5*c = 6025