Three years ago, Madison High School started charging an admission fee for basketball games to raise money for new bleachers. The initial price was `$2` per person, the school raised the price of admission to `$2.50` this year. Assuming this tread continuse, which of the following equations can be used to describe c, the cost of admission, y years after the school began charging for admission to games ?

Options

A. `c =6y+2`
B. `c = y/6+2.5`
C. `c = y/6+2`
D. `c = y/2+2`

Explanation

To solve the problem, we need to determine the equation that describes the cost of admission, \( c \), in terms of the number of years, \( y \), after the school began charging for admission to games.

### Step-by-Step Solution:

1. **Identify the Initial Cost**:
The initial admission fee when the school started charging was $2.

\[ \text{Initial Cost} = 2 \]

2. **Identify the Cost After Three Years**:
After three years, the admission fee increased to $2.50.

\[ \text{Cost After 3 Years} = 2.50 \]

3. **Calculate the Increase in Cost Over Three Years**:
The increase in cost over three years is:

\[ \text{Increase} = 2.50 - 2 = 0.50 \]

4. **Determine the Annual Increase**:
Since the increase of $0.50 occurs over three years, the annual increase is:

\[ \text{Annual Increase} = \frac{0.50}{3} = \frac{1}{6} \text{ dollars per year} \]

5. **Express the Increase in Terms of Years**:
If \( y \) is the number of years after the school began charging, the total increase in cost after \( y \) years is:

\[ \text{Total Increase} = \frac{1}{6}y \]

6. **Formulate the Equation for Cost**:
The total cost of admission \( c \) after \( y \) years can be expressed as the initial cost plus the total increase:

\[ c = 2 + \frac{1}{6}y \]

### Final Equation:
Thus, the equation that describes the cost of admission \( c \) in terms of years \( y \) is:

\[ c = 2 + \frac{1}{6}y \]

### Answer:
The equation that can be used to describe the cost of admission \( c \) after \( y \) years is \( c = 2 + \frac{1}{6}y \).

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