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Find out how many cars the baseball team needs to wash before it starts making a profit. The team spent $75setting up the car wash, and they are charging $5 per car for a wash.A. Write an equation to represent the amount ofmoney collected in dollars, y, in terms of the numberof cars washed, x. Ignore the setup cost. 𝑦 = 𝑥B. What do you need to do to the equation in part Ato account for the setup cost?To account for the setup cost, you need to_______add _______subtract 75 from the right sideof the equation obtained in part A.C. Write an equation representing the profit madeon the car wash in dollars, y, in terms of the numberof cars washed, x, after expenses. 𝑦 = 𝑥D. What is the value of the profit when the baseballteam washes 0 cars? What point represents thisvalue? What does the y-value of this point mean interms of the problem?E. How many cars does the baseball team have towash to break even? What point represents thisvalue? What does the x-value of this point mean interms of the problem?

Question

Find out how many cars the baseball team needs to wash before it starts making a profit. The team spent 75settingupthecarwash,andtheyarecharging75setting up the car wash, and they are charging 5 per car for a wash.A. Write an equation to represent the amount ofmoney collected in dollars, y, in terms of the numberof cars washed, x. Ignore the setup cost. 𝑦 = 𝑥B. What do you need to do to the equation in part Ato account for the setup cost?To account for the setup cost, you need to_______add _______subtract 75 from the right sideof the equation obtained in part A.C. Write an equation representing the profit madeon the car wash in dollars, y, in terms of the numberof cars washed, x, after expenses. 𝑦 = 𝑥D. What is the value of the profit when the baseballteam washes 0 cars? What point represents thisvalue? What does the y-value of this point mean interms of the problem?E. How many cars does the baseball team have towash to break even? What point represents thisvalue? What does the x-value of this point mean interms of the problem?

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Solution

A. The equation to represent the amount of money collected in dollars, y, in terms of the number of cars washed, x, ignoring the setup cost would be y = 5x. This is because each car wash costs $5.

B. To account for the setup cost, you need to subtract 75 from the right side of the equation obtained in part A. This is because the team spent $75 setting up the car wash, which is a cost they need to cover.

C. The equation representing the profit made on the car wash in dollars, y, in terms of the number of cars washed, x, after expenses would be y = 5x - 75. This equation takes into account both the income from washing cars and the initial setup cost.

D. The value of the profit when the baseball team washes 0 cars is -75.Thisisrepresentedbythepoint(0,75).Theyvalueofthispointmeansthattheteamisatalossof75. This is represented by the point (0, -75). The y-value of this point means that the team is at a loss of 75 if they do not wash any cars, due to the initial setup cost.

E. To find out how many cars the baseball team has to wash to break even, we set y = 0 in the equation from part C and solve for x. This gives us 0 = 5x - 75, which simplifies to x = 75/5 = 15. So, the team needs to wash 15 cars to break even. This is represented by the point (15, 0). The x-value of this point means that the team needs to wash 15 cars to cover their initial setup cost and start making a profit.

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