Ticket prices for a school play are $7.50 for students and $10.00 for adults . For a given performance , 200 tickets were sold , and the performance took in $1,775. Solving which of the following systems of equations yields the number of student tickets , x , and the number of adult ticket , y, that were bought for that performance ?

Options

A. x+y=200
7.5x+10y=1,775
B. x+y=1,775
7.5x+10y=200
C. x+y=200
`7.5x+10y=(1,775)/2`
D. x+y=1,775
7.5x+10y=(1,775)(2)

Answer

To solve the problem, we need to set up a system of equations based on the information given about ticket sales for a school play.

### Step 1: Define Variables
Let:
- \( x \) = number of student tickets sold
- \( y \) = number of adult tickets sold

### Step 2: Set Up the First Equation
According to the problem, the total number of tickets sold is 200. Therefore, we can write the first equation as:
\[ x + y = 200 \]

### Step 3: Set Up the Second Equation
The total revenue from ticket sales is $1,775. The revenue from student tickets is \( 7.50x \) and from adult tickets is \( 10.00y \). Thus, we can write the second equation as:
\[ 7.5x + 10y = 1775 \]

### Step 4: Write the System of Equations
Now we have the following system of equations:
1. \( x + y = 200 \)
2. \( 7.5x + 10y = 1775 \)

### Step 5: Solve the System of Equations
We can solve this system using substitution or elimination. Here, we will use substitution.

From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 200 - x \]

Now, substitute \( y \) in the second equation:
\[ 7.5x + 10(200 - x) = 1775 \]

### Step 6: Simplify and Solve for \( x \)
Distributing the 10:
\[ 7.5x + 2000 - 10x = 1775 \]

Combine like terms:
\[ -2.5x + 2000 = 1775 \]

Subtract 2000 from both sides:
\[ -2.5x = 1775 - 2000 \]
\[ -2.5x = -225 \]

Now, divide by -2.5:
\[ x = \frac{-225}{-2.5} = 90 \]

### Step 7: Solve for \( y \)
Now substitute \( x \) back into the equation for \( y \):
\[ y = 200 - x = 200 - 90 = 110 \]

### Final Answer
Thus, the number of student tickets sold is \( x = 90 \) and the number of adult tickets sold is \( y = 110 \).