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.

Question

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.
Remaining Attempts : 3

Answer 1

To determine the difference in price between Lorna and Lupe each purchasing 5 rings separately versus making one purchase of 10 rings, we will evaluate the cost using the provided piecewise function \( f(x) \).

1. Calculating the cost for 5 rings each:
   Since \( x = 5 \) falls within the range \( 4 \leq x \leq 7 \), we will use the function \( f(x) = 1.5x \).

   For 5 rings: \[ f(5) = 1.5 \times 5 = 7.5 \] Each person pays $7.50 for 5 rings. Therefore, for two people: \[ \text{Total cost for Lorna and Lupe} = 7.5 + 7.5 = 15 \]

2. Calculating the cost for 10 rings in a single purchase:
   Since \( x = 10 \) falls within the range \( x \geq 8 \), we will use the function \( f(x) = 1.25x \).

   For 10 rings: \[ f(10) = 1.25 \times 10 = 12.5 \]

3. Calculating the difference in price:
   Now, we find the difference in cost: \[ \text{Difference} = \text{Cost for two separate purchases} - \text{Cost for one purchase} \] \[ \text{Difference} = 15 - 12.5 = 2.5 \]

4. Final Answer:
   Lorna and Lupe would save a total of $2.50 if they made one purchase of 10 rings.