Questions: Tickets to a basketball game can be ordered online for a set price per ticket plus a 5.50 service fee. The total cost in dollars for ordering 5 tickets is 108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased). c(x)=5.50+20.50 x c(x)=5.50 x+20.50 c(x)=5.50+21.60 x c(x)=5.50 x+21.60

Tickets to a basketball game can be ordered online for a set price per ticket plus a 5.50 service fee. The total cost in dollars for ordering 5 tickets is 108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
c(x)=5.50+20.50 x
c(x)=5.50 x+20.50
c(x)=5.50+21.60 x
c(x)=5.50 x+21.60

Transcript text: Tickets to a basketball game can be ordered online for a set price per ticket plus a $\$ 5.50$ service fee. The total cost in dollars for ordering 5 tickets is $\$ 108.00$. Which linear function represents $c$, the total cost, when $x$ tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased). $c(x)=5.50+20.50 x$ $c(x)=5.50 x+20.50$ $c(x)=5.50+21.60 x$ $c(x)=5.50 x+21.60$

Solution

Solution Steps

Step 1: Identify the given information

The problem states that the total cost $ c $ for ordering $ x $ tickets includes a set price per ticket plus a \$5.50 service fee. The total cost for 5 tickets is \$108.00.

Step 2: Set up the equation

Let the price per ticket be $ p $. The total cost $ c $ can be expressed as: \[ c = 5.50 + p \cdot x \] For $ x = 5 $, the total cost is \$108.00: \[ 108.00 = 5.50 + p \cdot 5 \]

Step 3: Solve for the price per ticket

Subtract \$5.50 from both sides of the equation: \[ 108.00 - 5.50 = 5p \] \[ 102.50 = 5p \] Divide both sides by 5: \[ p = \frac{102.50}{5} = 20.50 \]

Step 4: Write the linear function

Substitute $ p = 20.50 $ into the equation for $ c $: \[ c(x) = 5.50 + 20.50x \]