Question

Grace and her family are planning a trip to the amusement park. The piecewise function includes the prices for each ticket purchased, which is dependent on the total number of tickets, x, purchased. What would be the total cost to purchase tickets for a family of 5?

f(x)=⎧⎩⎨⎪⎪35,30,25, 1≤x≤56≤x≤10x≥11

(1 point)
Responses

$175
$175

$35
$35

$125
$125

$150

Answer 1

To find the total cost for Grace and her family of 5, we will use the piecewise function given:

\[
f(x) =
\begin{cases}
35 & \text{if } 1 \leq x \leq 5 \\
30 & \text{if } 6 \leq x \leq 10 \\
25 & \text{if } x \geq 11
\end{cases}
\]

Since Grace's family consists of 5 people, we have \(x = 5\).

Now, we look at the piecewise function for \(x = 5\):

- Since \(5\) falls within the range \(1 \leq x \leq 5\), we use the first condition:

\[
f(5) = 35
\]

This means each ticket costs $35. If they are purchasing tickets for 5 people, the total cost will be:

\[
\text{Total Cost} = 5 \times 35 = 175
\]

Therefore, the total cost for purchasing tickets for a family of 5 is **$175**.