A theater teacher is going to order between 2 and 6 extra chairs for her classroom. The cost of the chairs, y, can be represented by y = 22x + 5.5 where x is the number of chairs ordered. Which best represents of the situation? a, 2 <= x <= 6 b. \{2, 3, 4, 5, 6\} c. \{49.5, 71.5, 93.5, 115.5, 137.5\} d. 49.5 <= y <= 137.5

Answer 1

To determine which option best represents the situation described, we need to analyze the function given and the constraints on the number of chairs ordered.

1. The cost of the chairs is given by the formula \( y = 22x + 5.5 \).

2. The number of chairs ordered, \( x \), can be between 2 and 6 (inclusive). Thus, we have the inequality \( 2 \leq x \leq 6 \).

3. We need to calculate the cost \( y \) for the minimum and maximum values of \( x \):

   • For \( x = 2 \): \[ y = 22(2) + 5.5 = 44 + 5.5 = 49.5 \]

   • For \( x = 6 \): \[ y = 22(6) + 5.5 = 132 + 5.5 = 137.5 \]

4. The resulting range for \( y \) is from \( 49.5 \) to \( 137.5 \), which gives us \( 49.5 \leq y \leq 137.5 \).

Now let's evaluate the options:

a. \( 2 \leq x \leq 6 \) - This correctly represents the range of \( x \).

b. \( {2, 3, 4, 5, 6} \) - This is a discrete set of values for \( x \) between 2 and 6.

c. \( {49.5, 71.5, 93.5, 115.5, 137.5} \) - This is a discrete set of values for \( y \) corresponding to some values of \( x \).

d. \( 49.5 \leq y \leq 137.5 \) - This accurately represents the range of values for \( y \) based on the minimum and maximum calculations.

The best representations for the situation are d and a. However, if we need a single best answer representing the cost \( y \), then the answer is:

d. \( 49.5 \leq y \leq 137.5 \).