The seventh graders sold tickets to their play.the tickets cost $3 for students and $6 for adults. For one performance they sold 79 tickets and collected $375. How many student tickets and how many adult tickets were sold? Write the equation and solve, showing all of your steps.
student tickets --- x
adult tickets ---- 79-x
solve for x
3x + 6(79-x) = 375
How many student tickets and how many adult tickets were sold? @ REINY YOU GAVE THE TOTAL COLLECTED
To find the number of student tickets and adult tickets sold, we can set up a system of equations.
Let's say the number of student tickets sold is "s" and the number of adult tickets sold is "a".
According to the information given, the total number of tickets sold is 79, so we can write the equation: s + a = 79 ...(Equation 1)
Also, the total amount collected from ticket sales is $375, with each student ticket priced at $3 and each adult ticket priced at $6. So, we can write the equation: 3s + 6a = 375 ...(Equation 2)
Now, we have a system of two equations with two variables. We can solve this system to find the values of "s" and "a".
To solve the system, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve Equation 1 for "s":
s = 79 - a
Step 2: Substitute the value of "s" in Equation 2:
3(79 - a) + 6a = 375
Distribute: 237 - 3a + 6a = 375
Combine like terms: 3a = 375 - 237
Simplify: 3a = 138
Step 3: Solve for "a":
a = 138 / 3
a = 46
Step 4: Substitute the value of "a" back into Equation 1 to solve for "s":
s + 46 = 79
s = 79 - 46
s = 33
Therefore, 33 student tickets and 46 adult tickets were sold.