After the booster club sold 40 hot dogs at a football game, it had $90 in profit. After the next game, it had sold a total of 80 hot dogs and had a total of $210 in profit. Which equation models the total profit,y,based on the number of hotdogs sold,x

Given : After the booster club sold 40 hot dogs at a football game, it had $90 in profit. After the next game, it had sold a total of 80 hot dogs and had a total of $210 in profit.

To find : Which equation models the total profit,y,based on the number of hot dogs sold,x ?

Solution :

Let x = total number of hot dogs sold

y = total profit from total sales of hot dogs

We can model the equation: [tex]y = m x + b[/tex] ......[A]

where, y is the total profit and x is the number of hot dogs sold.

Profit for 40 hot dogs = $90 profit

The system of equation form is

[tex]90 =40m + b[/tex] ......[1]

Profit for 80 hot dogs = $210 profit

The system of equation form is

[tex]210 =80m + b[/tex] .......[2]

The solution of equations [1] and [2]

Subtract equation [1] and [2]

[tex]210-90 = 80m-40m + b-b[/tex]

[tex]120 = 40m[/tex]

[tex]\frac{120}{40} = m[/tex]

[tex]3 = m[/tex]

Substitute in equation [1]

[tex]90 =40(3) + b[/tex]

[tex]90 =120+ b[/tex]

[tex]b=-30[/tex]

Substitute the values in equation [A]

[tex]y = 3x-30[/tex]

This is the required equation models the total profit based on number of hot dogs.