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.

Answer 1

To determine the difference in cost between Lorna and Lupe purchasing 5 rings each versus a single purchase of 10 rings, we need to calculate the costs using the piecewise function you've provided.

Given the function:

\[
f(x) =
\begin{cases}
2x & \text{if } 0 \leq x \leq 3 \\
1.5x & \text{if } 4 \leq x \leq 7 \\
1.25x & \text{if } x \geq 8
\end{cases}
\]

1. **Calculating the cost for Lorna and Lupe each purchasing 5 rings:**

Since 5 is within the range \(4 \leq x \leq 7\):
\[
f(5) = 1.5 \times 5 = 7.5 \text{ dollars}
\]
Therefore, the total for both Lorna and Lupe purchasing 5 rings each:
\[
\text{Total cost for Lorna and Lupe} = 7.5 + 7.5 = 15 \text{ dollars}
\]

2. **Calculating the cost for one purchase of 10 rings:**

Since 10 is greater than 8:
\[
f(10) = 1.25 \times 10 = 12.5 \text{ dollars}
\]

3. **Finding the difference in price:**

The difference in price if they each separately purchase 5 rings compared to making one purchase of 10 rings is:
\[
\text{Difference} = \text{Total for 5 rings each} - \text{Total for 10 rings}
\]
\[
\text{Difference} = 15 - 12.5 = 2.5 \text{ dollars}
\]

Thus, rounding to the nearest cent, they would save a total of **$2.50** if they made one purchase of 10 rings.