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.

2x, 0 ≤ x ≤ 3
f(x) = 1.5x, 4 ≤ x ≤ 7
(1.25x, x > 8

(1 point)
They would save a total of $_ if they made one purchase of 10 rings.

Answer 1

Let's calculate the cost for Lorna and Lupe if they each purchase 5 rings separately, and then compare that to the cost of buying 10 rings at once.

### Step 1: Calculate Cost for 5 Rings Each
Since they each want to purchase 5 rings, we need to determine the cost based on the piecewise function given.

For \(x = 5\):
- The cost function applies as \(f(x) = 1.5x\) because \(4 \leq x \leq 7\).

Calculating \(f(5)\):
\[
f(5) = 1.5 \times 5 = 7.5
\]

Thus, the cost for each person buying 5 rings is $7.50.

Since both Lorna and Lupe are buying 5 rings each, the total cost for them together is:
\[
7.5 + 7.5 = 15.00
\]

### Step 2: Calculate Cost for 10 Rings in One Purchase
Now we will calculate the cost if they make one purchase of 10 rings. For \(x = 10\), we refer to the cost function of \(x > 8\), which is:
- \(f(x) = 1.25x\).

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

### Step 3: Find the Difference in Price
Now we will find the difference in price between the two purchasing strategies:
- Total cost if each buys 5 rings: $15.00
- Total cost if they buy 10 rings together: $12.50

Calculating the savings:
\[
\text{Savings} = 15.00 - 12.50 = 2.50
\]

### Final Answer
They would save a total of $2.50 if they made one purchase of 10 rings.