Question

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?

Answer 1

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

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.