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
$35
$35
$125
$125
$150
$150
$175
f(x)=⎧⎩⎨⎪⎪35,30,25, 1≤x≤56≤x≤10x≥11
(1 point)
Responses
$35
$35
$125
$125
$150
$150
$175
Answers
GPT-4o mini
To determine the total cost for a family of 5, we need to use the piecewise function provided:
\[
f(x) =
\begin{cases}
35 & \text{if } 1 \leq x \leq 5 \\
30 & \text{if } 6 \leq x \leq 10 \\
25 & \text{if } x \geq 11
\end{cases}
\]
Since Grace's family is purchasing 5 tickets, we are in the first case where \(1 \leq x \leq 5\). According to the function, for this range of \(x\), the cost for each ticket is $35.
Now, to find the total cost for 5 tickets, we calculate:
\[
\text{Total Cost} = 5 \times 35 = 175
\]
Therefore, the total cost to purchase tickets for a family of 5 is **$175**.
\[
f(x) =
\begin{cases}
35 & \text{if } 1 \leq x \leq 5 \\
30 & \text{if } 6 \leq x \leq 10 \\
25 & \text{if } x \geq 11
\end{cases}
\]
Since Grace's family is purchasing 5 tickets, we are in the first case where \(1 \leq x \leq 5\). According to the function, for this range of \(x\), the cost for each ticket is $35.
Now, to find the total cost for 5 tickets, we calculate:
\[
\text{Total Cost} = 5 \times 35 = 175
\]
Therefore, the total cost to purchase tickets for a family of 5 is **$175**.