a choral group sells a total of 225 tickets to its first show. A student ticket costs $5. An adult ticket costs $8. Total ticket sales are $1,425. How many of each type of ticket were sold?
to get that, solve
s+a = 225
5s+8a = 1425
To determine the number of each type of ticket sold, let's assign variables.
Let's say X represents the number of student tickets sold.
And let's say Y represents the number of adult tickets sold.
We are given two pieces of information:
1) The total number of tickets sold is 225.
2) The total ticket sales amount to $1,425.
Based on the given information, we can form two equations to solve this problem.
Equation 1: X + Y = 225
This equation represents the total number of tickets sold.
Equation 2: (5X) + (8Y) = 1,425
This equation represents the total ticket sales amount.
To solve this system of equations, we can use either substitution or elimination method. In this case, let's use the elimination method.
Rewriting Equation 1 as X = 225 - Y, we substitute this expression for X in Equation 2:
5(225 - Y) + 8Y = 1,425
Simplifying the equation:
1,125 - 5Y + 8Y = 1,425
3Y = 1,425 - 1,125
3Y = 300
Y = 300 / 3
Y = 100
Now, substitute Y = 100 back into Equation 1:
X + 100 = 225
X = 225 - 100
X = 125
Therefore, 125 student tickets and 100 adult tickets were sold.