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.

student tickets

adult tickets

Answer 1

To solve this problem, we will set up a system of equations based on the information given about ticket sales.

Let:
- \( s \) = number of student tickets sold
- \( a \) = number of adult tickets sold

We can create the following equations:

1. From the total number of tickets sold:
\[
s + a = 150
\]

2. From the total amount of money collected:
\[
3s + 8a = 1000
\]

Now we will use the substitution method to solve this system of equations.

### Step 1: Solve the first equation for one variable
From the first equation, solve for \( s \):
\[
s = 150 - a
\]

### Step 2: Substitute \( s \) into the second equation
Now, substitute \( s \) in the second equation:
\[
3(150 - a) + 8a = 1000
\]

### Step 3: Distribute and simplify
Distributing \( 3 \):
\[
450 - 3a + 8a = 1000
\]
Combine like terms:
\[
450 + 5a = 1000
\]

### Step 4: Solve for \( a \)
Subtract \( 450 \) from both sides:
\[
5a = 1000 - 450
\]
\[
5a = 550
\]
Now, divide by \( 5 \):
\[
a = 110
\]

### Step 5: Use the value of \( a \) to find \( s \)
Now substitute \( a \) back into the equation for \( s \):
\[
s = 150 - a = 150 - 110 = 40
\]

### Final Answer
- Student tickets sold: **40**
- Adult tickets sold: **110**

So, the number of student tickets sold is **40**, and the number of adult tickets sold is **110**.