Question

Tickets to a school play cost $3 for students and $8 for adults. on opening night, $1,000 was collected and 150 tickets sold. use substitution to solve a system of equations to find how many of each kind of ticket were sold? enter your answers in the boxes.

Answer 1

To find out how many of each kind of ticket were sold, we can set up a system of equations and solve them using substitution. The number of student tickets sold is 40 and the number of adult tickets sold is 110.

Step-by-step explanation:

To find out how many of each type of ticket were sold, we can set up a system of equations using the given information. Let's represent the number of student tickets sold as 's' and the number of adult tickets sold as 'a'.

The total revenue collected from the ticket sales can be expressed as: 3s + 8a = 1000

And the total number of tickets sold can be expressed as: s + a = 150

Now, using substitution, we can solve the system of equations. Solving the second equation for 's', we get s = 150 - a. Substituting this value of 's' into the first equation, we have: 3(150 - a) + 8a = 1000

Simplifying the equation, we get: 450 - 3a + 8a = 1000

Combining like terms, we get: 5a = 550

Dividing both sides by 5, we get: a = 110

Substituting this value of 'a' back into the second equation, we can find the value of 's': s + 110 = 150

Simplifying the equation, we get: s = 150 - 110

Therefore, the number of student tickets sold (s) is 40, and the number of adult tickets sold (a) is 110.

Answer 2

s+a=150
3s+8a=1000
a=-s+150
3s-8s+1200=1000
-5s=-200
s=40
a=110
40 student and 110 adult tickets were sold