Question

1. the function $c(x) = 17.5x - 10$ represents the cost (in dollars) of buying $x$ tickets to the orchestra with a $10 coupon.

a) how much does it cost to buy five tickets?
b) how many tickets can you buy with $130?

Explanation:

Part (a)

Step1: Identify the value of \( x \)

We need to find the cost for 5 tickets, so \( x = 5 \).

Step2: Substitute \( x = 5 \) into the function \( C(x) \)

The function is \( C(x)=17.5x - 10 \). Substitute \( x = 5 \):
\( C(5)=17.5\times5 - 10 \)

Step3: Calculate the value

First, calculate \( 17.5\times5 = 87.5 \). Then subtract 10: \( 87.5-10 = 77.5 \).

Step1: Set \( C(x) = 130 \)

We know the cost \( C(x) = 130 \), so we set up the equation \( 17.5x - 10=130 \).

Step2: Solve for \( x \)

First, add 10 to both sides of the equation: \( 17.5x=130 + 10=140 \).
Then, divide both sides by 17.5: \( x=\frac{140}{17.5}=8 \).

Answer:

The cost to buy five tickets is \(\$77.5\).

Part (b)