Ariel enters a contest to sel advertisements in ther school's yearbook. To qualify for a prize. She has to sell at least `$1,500` worth of advertisements consisting of no fewer than 15 invididual ads. Each full-page ad costs `$110,` each half-page and costs `$70,` and each quarter-page ad costs `%50.` Which of the following systems of inequalities represents this situation, whre x is the number of full-page ads she sells, y is the number of half-page ads she sells, and z is the number of quarter-page ads she sells?

Options

A. `110x + 70y + 50zge 1,500`
`x+y+z le 15`
B. `110x +70y+50z le 1,500`
`x +y +z le 15`
C. `110x + 70 y + 50z ge 1,500`
`x +y +z ge 15`
D. `110x + 70 y + 50z le 1,500`
`x +y + z ge 15`

Explanation

To solve the problem, we need to formulate a system of inequalities based on the conditions provided.

1. **Understanding the Variables**:
- Let \( x \) be the number of full-page ads sold.
- Let \( y \) be the number of half-page ads sold.
- Let \( z \) be the number of quarter-page ads sold.

2. **Setting Up the First Inequality**:
- Each full-page ad costs $110, so the total revenue from full-page ads is \( 110x \).
- Each half-page ad costs $70, so the total revenue from half-page ads is \( 70y \).
- Each quarter-page ad costs $50, so the total revenue from quarter-page ads is \( 50z \).
- Ariel needs to sell at least $1,500 worth of advertisements. Therefore, we can write the first inequality as:
\[ 110x + 70y + 50z \geq 1500 \]

3. **Setting Up the Second Inequality**:
- Ariel must sell no fewer than 15 individual ads. This means the total number of ads sold (full-page, half-page, and quarter-page) must be at least 15. Thus, we can write the second inequality as:
\[ x + y + z \geq 15 \]

4. **Combining the Inequalities**:
- We now have two inequalities that represent the situation:
1. \( 110x + 70y + 50z \geq 1500 \)
2. \( x + y + z \geq 15 \)

5. **Final System of Inequalities**:
- The system of inequalities that represents the situation is:
\[ \begin{align*} 110x + 70y + 50z & \geq 1500 \\ x + y + z & \geq 15 \end{align*} \]