Question

the total cost, y, for x passes to the state fair includes a flat fee for processing and a cost per pass. one family purchased 5 passes for a total cost of $390. another family purchased 8 passes for $615.\which linear equation represents the total cost in dollars, y, for x passes?\\a. $y = 78x$\\b. $y = 75x + 15$\\c. $y = 76.88x$\\d. $y = 15x + 75$

Explanation:

Step1: Define linear equation form

Let the linear equation be $y = mx + b$, where $m$ is cost per pass, $b$ is flat fee.

Step2: Set up system of equations

From given data:
$$390 = 5m + b$$
$$615 = 8m + b$$

Step3: Subtract equations to find m

Subtract first equation from second:
$$615 - 390 = (8m + b) - (5m + b)$$
$$225 = 3m$$
$$m = \frac{225}{3} = 75$$

Step4: Substitute m to find b

Plug $m=75$ into $390 = 5m + b$:
$$390 = 5(75) + b$$
$$390 = 375 + b$$
$$b = 390 - 375 = 15$$

Step5: Form final equation

Substitute $m=75$ and $b=15$ into $y=mx+b$.

Answer:

B. $y=75x+15$