<p>Problem 2.1b – Estimating Profit</p><p>At their planning meeting, the organizers of the walkathon discussed the following expenses and income.</p><p> Expense for posters and newspaper, radio, and TV ads: $5000.  Expense for Souvenir T-shirts for participants: $6 per child and $8.50 per adult  Income from business sponsors whose logos will appear on T-shirts and signs: $10,000.  Expense for paramedics and an ambulance in case of emergency: $2500  Income from registration fees: $5 per child, $15 per adult.</p><p>A. Find the total income, total expenses, and the total profit if 40 children and 30 adults participate in the walkathon. Show all of your work in an organized fashion. Use your calculator only where absolutely necessary. (Remember profit is found by subtracting expenses from income.) Show all of your work.</p><p>B. Write an expression for the total income in terms of the number of adults, a, and the number of children, c, who participate. </p><p>C. Write an expression for the total expenses in terms of the number of adults, a, and the number of children, c, who participate. Check with the teacher after you have written this to make sure that your answers to B and C are correct.</p><p>D. Use parentheses and your results from parts B and C to write an expression showing the profit as total income minus total expenses. That is, express the profit as (expression for income) – (expression for expenses). </p><p>E. Simplify your an expression for profit to come up with an expression that is equivalent to your expression, but is easier to work with. Use the distributive property and combining like terms to show that the two profit expressions are equivalent. F. Evaluate your profit expressions from parts D and E for a = 100 and c = 75. Can you conclude from your results that the expressions are equivalent? Show work and explain.</p><p>G. Compare the profit expressions you wrote in parts D and E. What are the advantages and disadvantages of writing the profit expression in a shorter form?</p>