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)=left{\begin{array}{l} 2 x, quad 0<x<3 \\ 1.5 x, quad 4<x<7 \\ 1.25 x, quad x geq 8 end{array}
ight.
(1 point)
they would save a total of $ square $ if they made one purchase of 10 rings.
check answer remaining attempts 3

Explanation:

Step1: Calculate the cost if purchased separately

Lorna and Lupe each want to purchase 5 rings. So the total number of rings when purchased separately is \(5 + 5=10\) rings.
Since \(10\gt8\), for the separate - purchase case, we use the function \(f(x)=1.25x\) (where \(x = 10\)).
The cost \(C_1\) when purchased separately is \(C_1=1.25\times10 = 12.5\) dollars.

Step2: Calculate the cost if purchased as one

If they make one purchase of \(x = 10\) rings (since \(10\gt8\)), we use the function \(f(x)=1.25x\).
The cost \(C_2\) when purchased as one is also \(C_2 = 1.25\times10=12.5\) dollars. Wait, no, there was a mis - understanding.
Wait, when purchased separately: Lorna buys 5 rings (\(4\lt5\lt7\)), so \(f(5)=1.5\times5 = 7.5\) dollars for Lorna. Lupe buys 5 rings (\(4\lt5\lt7\)), so \(f(5)=1.5\times5 = 7.5\) dollars for Lupe. The total cost when purchased separately \(C_1=7.5 + 7.5=15\) dollars.
When purchased as one ( \(x = 10\gt8\)), the cost \(C_2=1.25\times10 = 12.5\) dollars.

Step3: Calculate the savings

The savings \(S\) is \(S=C_1 - C_2\).
Substitute \(C_1 = 15\) and \(C_2 = 12.5\) into the formula: \(S=15−12.5 = 2.5\) dollars.

Answer:

\(2.50\)