Tickets to a basketball game were $2.50 each for students and $4.25 each for adults. if a total of 183 tickets were sold and $538 was collected from the ticket sales, then how many of each type of ticket were sold?
Let's establish our unknown numbers with the variables x and y:
x amount of students y amount of parents
We can establish these equasions:
x + y = 183 (number of students + number of parents) 2.50x + 4.25y = 538 (the amount each group paid)
To make things easier, we can put x or y from the first equasion on to the right side of that same equasion. I switched x in my case [tex]x + y = 183 \\ y = 183 - x[/tex] We insert that into our second equasion and solve it [tex]2.50x + 4.25(183 - x) = 538 \\ 2.50x + 777.75 - 4.25x = 538 \\ 2.50x - 4.25x = 538 - 777.75 \\ - 1.75x = - 239.75 \\ x = \frac{ - 239.75}{ - 1.75} \\ x = 137[/tex] We now know that x = 137. If the total is 183, we just have to subtract 137 from that number to find out the value of y [tex]183 - 137 = 46[/tex] RESULT: x = 137 ==> 137 student tickets sold y = 46 ==> 46 adult tickets sold
