Amistad starts selling tickets to basketball games. They sell 292 tickets to the last game of the season. An adult ticket costs $3. A student ticket costs $1. They collect $470.00 in ticket sales. Write and solve a system of equations to find the number of each ticket sold.
To find the number of adult and student tickets sold, we can set up a system of equations.
Let's denote the number of adult tickets as "A" and the number of student tickets as "S."
Based on the given information, we can set up two equations:
Equation 1: A + S = 292 (since they sold a total of 292 tickets)
Equation 2: 3A + 1S = 470 (since the total ticket sales amount to $470.00)
To solve this system of equations, we can use the method of substitution or elimination.
Using the substitution method:
From Equation 1, we can rewrite it as A = 292 - S.
Substituting this value of A into Equation 2:
3(292 - S) + 1S = 470
876 - 3S + S = 470
-2S = 470 - 876
-2S = -406
S = -406 / -2
S = 203
Now that we have the value of S, we can substitute it back into Equation 1 to find A:
A + 203 = 292
A = 292 - 203
A = 89
Therefore, the number of adult tickets sold is 89, and the number of student tickets sold is 203.
a+s = 292
3a+1s = 470
2a = 178
a = 89
s = 203
check: 3*89 + 203 = 470