Question
Question
Lorna and Lupe are playing a ring toss game at the fair. The cost to play the game depends on the number of rings purchased. The cost is described in the piecewise function, where x is the number of rings purchased. Lorna and Lupe each want to purchase 5 rings. What is the difference in price if they each separately purchase 5 rings compared to making one purchase of 10 rings? Round the answer to the nearest cent.
f(x)=⎧⎩⎨⎪⎪2x,1.5x,1.25x, 0≤x≤34≤x≤7x≥8
(1 point)
They would save a total of $
if they made one purchase of 10 rings.
Lorna and Lupe are playing a ring toss game at the fair. The cost to play the game depends on the number of rings purchased. The cost is described in the piecewise function, where x is the number of rings purchased. Lorna and Lupe each want to purchase 5 rings. What is the difference in price if they each separately purchase 5 rings compared to making one purchase of 10 rings? Round the answer to the nearest cent.
f(x)=⎧⎩⎨⎪⎪2x,1.5x,1.25x, 0≤x≤34≤x≤7x≥8
(1 point)
They would save a total of $
if they made one purchase of 10 rings.
Answers
GPT-4o mini
To determine the pricing using the piecewise function provided, we first need to calculate the cost for each scenario: separately purchasing 5 rings each and making one purchase of 10 rings.
The piecewise function is defined as follows:
- \( f(x) = 2x \) for \( 0 \leq x \leq 3 \)
- \( f(x) = 1.5x \) for \( 4 \leq x \leq 7 \)
- \( f(x) = 1.25x \) for \( x \geq 8 \)
### Step 1: Cost for Lorna and Lupe purchasing 5 rings each
Since 5 rings fall in the range \( 4 \leq x \leq 7 \), we will use the second part of the piecewise function \( f(x) = 1.5x \).
Calculating the cost for one person (5 rings):
\[
f(5) = 1.5 \times 5 = 7.5
\]
Since there are two people making the same purchase:
\[
\text{Total cost for 5 rings each} = 7.5 + 7.5 = 15.00
\]
### Step 2: Cost for making one purchase of 10 rings
Since 10 rings fall in the range \( x \geq 8 \), we will use the third part of the piecewise function \( f(x) = 1.25x \).
Calculating the cost for 10 rings:
\[
f(10) = 1.25 \times 10 = 12.5
\]
### Step 3: Finding the Difference in Price
Now, we can find the difference in price between the two scenarios:
\[
\text{Difference} = \text{Total cost for 5 rings each} - \text{Cost for 10 rings}
\]
\[
\text{Difference} = 15.00 - 12.5 = 2.5
\]
### Final Answer
They would save a total of **$2.50** if they made one purchase of 10 rings.
The piecewise function is defined as follows:
- \( f(x) = 2x \) for \( 0 \leq x \leq 3 \)
- \( f(x) = 1.5x \) for \( 4 \leq x \leq 7 \)
- \( f(x) = 1.25x \) for \( x \geq 8 \)
### Step 1: Cost for Lorna and Lupe purchasing 5 rings each
Since 5 rings fall in the range \( 4 \leq x \leq 7 \), we will use the second part of the piecewise function \( f(x) = 1.5x \).
Calculating the cost for one person (5 rings):
\[
f(5) = 1.5 \times 5 = 7.5
\]
Since there are two people making the same purchase:
\[
\text{Total cost for 5 rings each} = 7.5 + 7.5 = 15.00
\]
### Step 2: Cost for making one purchase of 10 rings
Since 10 rings fall in the range \( x \geq 8 \), we will use the third part of the piecewise function \( f(x) = 1.25x \).
Calculating the cost for 10 rings:
\[
f(10) = 1.25 \times 10 = 12.5
\]
### Step 3: Finding the Difference in Price
Now, we can find the difference in price between the two scenarios:
\[
\text{Difference} = \text{Total cost for 5 rings each} - \text{Cost for 10 rings}
\]
\[
\text{Difference} = 15.00 - 12.5 = 2.5
\]
### Final Answer
They would save a total of **$2.50** if they made one purchase of 10 rings.