Question

the total cost, y, for x tickets to a concert includes a flat fee for processing and a cost per ticket. one customer purchased 4 tickets for a total cost of $160. another customer purchased 8 tickets for a total cost of $300. which linear equation represents the total cost in dollars, y, for x tickets? y = 20x + 35 y = 40x y = 35x + 20 y = 37.5x

Explanation:

Step1: Set up equations

Let the cost - per - ticket be $m$ and the flat - fee be $b$. The linear equation is $y=mx + b$. Using the given information:
When $x = 4$, $y = 160$, so $160=4m + b$. When $x = 8$, $y = 300$, so $300=8m + b$.

Step2: Solve for $m$

Subtract the first equation from the second equation:
$(8m + b)-(4m + b)=300 - 160$.
$8m + b-4m - b=140$.
$4m=140$, then $m = 35$.

Step3: Solve for $b$

Substitute $m = 35$ into the first equation $160=4m + b$:
$160=4\times35 + b$.
$160 = 140 + b$.
$b=160 - 140=20$.

Step4: Write the linear equation

The linear equation is $y = 35x+20$.

Answer:

$y = 35x + 20$