 # 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$21

Mathematics

## Question

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

• ### 1. User Answers leiinmain

The correct answer would be: y-90=3(x-40)
• ### 2. User Answers tardymanchester

Required equation $$y = 3x-30$$

Step-by-step explanation:

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: $$y = m x + b$$ ......[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 $$90 =40m + b$$ ...... Profit for 80 hot dogs =$210 profit

The system of equation form is

$$210 =80m + b$$ .......

The solution of equations  and 

Subtract equation  and 

$$210-90 = 80m-40m + b-b$$

$$120 = 40m$$

$$\frac{120}{40} = m$$

$$3 = m$$

Substitute in equation 

$$90 =40(3) + b$$

$$90 =120+ b$$

$$b=-30$$

Substitute the values in equation [A]

$$y = 3x-30$$

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