after the booster club sold 40 hotdogs at a football game, it had $90 in profit. after the next football game, it has sold a total of 80 hotdogs and had a total of $210 in profit. which equation models the total profit, y, based on the number of hotdogs sold, x?

The required equation models the total profit, y, based on the number of hot dogs sold, x is y = 3 x - 30.

Step-by-step explanation:

Let x = total number of hot dogs sold

y = total profit from total sales of hot dogs

The given situation can be written as: y = m x + C ... [A]

Now, Profit for 40 hot dogs = $90 profit

So, here this can be written as:

90 = 40 m + C ... [1]

Profit for 80 hot dogs = $210 profit

So, here this can be written as:

210 = 80 m + C ... [2]

Now, solving both the equations, we get:

Subtracting [1] and [2], we get

210 - 90 = 80 m + C - (40 m + C)

or, 120 = 40 m

or, m = 120/40 = 3

or, m = 3

Solving for the value of C, we get: C = - 30

Putting the value of m back in the equation : y = m x + C

y = 3 x - 30

Hence, the required equation models the total profit, y, based on the number of hot dogs sold, x is y = 3 x - 30.