a school's chorus bought 30 tickets to a play. total cost of tickets $98. if student tickets cost $3 and each adult tickets cost $5, how many adults are going with the chorus?
thanks
It's a system of equations
Let's say that students = x,and that adults = y
Now let's construct the system of equations:
x + y = 30
3x + 5y = 98
Let's work by substitution with the first equation:
x = 30 - y
Lets the expression above in the second equation:
3(30-y)+5y=98
Now we solve for y:
90-3y+5y=98
-3y+5y=98-90
2y=8
y = 8/2
y = 4
So we said that y represent the number of adults, so we have 4 adults.
30-4= 26 students
To find out how many adults are going with the chorus, we need to set up an equation based on the given information.
Let's assume the number of adult tickets purchased is "a" and the number of student tickets purchased is "s."
According to the given information, the total number of tickets purchased is 30. So, we can write the following equation:
a + s = 30 (Equation 1)
We also know that the total cost of the tickets purchased is $98. Since adult tickets cost $5 and student tickets cost $3, we can create another equation based on the total cost:
5a + 3s = 98 (Equation 2)
We now have a system of two equations. To solve it, we can use the method of substitution or elimination. Let's solve it using the substitution method:
1. Solve Equation 1 for a:
a = 30 - s
2. Substitute the value of "a" in Equation 2:
5(30 - s) + 3s = 98
3. Simplify the equation:
150 - 5s + 3s = 98
150 - 2s = 98
4. Rearrange the equation:
-2s = 98 - 150
-2s = -52
5. Divide both sides by -2:
s = (-52) / (-2)
s = 26
Now that we have the number of student tickets, we can substitute this value back into Equation 1 to find the number of adult tickets:
a + 26 = 30
Subtract 26 from both sides:
a = 30 - 26
a = 4
So, there are 4 adults going with the chorus.