3.2+Estimating+Profit++0910

CT Big Idea:Equations can be used to model real things Essential Question: What are the distributive and commutative properties useful for? Notes: In this problem you need to know certain information, - Expense for posters and newspaper,radio, and TV ads: $500 -Expense for souvenir T-shirts for participants: $6 per child, $8.50 per adult -Income from business sponsors whose logos will appear on the T-shirts and sign: $1000 -Expense for paramedics and an ambulance in case of emergency: $250 -Income from registration fees: $5 per child, $15 per adult

3.2

//**A**.// //**Estimate the total income, the total expense, and the total profit if 40 children and 30 adults participate in the Walkathon.**// If 40 children and 30 adults participate in the walkathoon there would be $450 of income + the $1000 from the sponsors, ($1450). Expenses would be $250+$500+ $240+$255= $1245. The profit would be $205.

//**B. Write two equivalent expressions for the total income in terms of number of adults, a, and the number of children, c, who participate.**// $1000+$5c+$15 a, and, $1000+(c*5)+(a*15)

//**C. Write two equivalent expressions for the total expense in terms of the number of adults,a, and the number of children,c, who participate.**// ($500+250)+(c*$6)+(a*$8.5) and $750 +$6c+$8.50a

//**D. Use brackets and your results from parts B and C to wrie an equivalent expression showing profit as total income minus total expenses. That is, express the profit as total income minus total expenses. That is, express the profit as (expression for income)-(expression for expenses).**// ($1000+$5c+$15a)-($750+6c+8.50a)


 * E. Write and expression for profit that is equivalent to your expression from part D but that is as short as possible. Use the distributive and commutative properties to show the two profit expressions are equivalent.**

$250-$1c+6.5a is equivalent to the expression in part D.

$250-$1c+6.5a = ($1000+5c+15a)-($750+6c+8.50a) $250-$10+$32.5 = ($1000+$50+$75)-($750+$60+$42.50) $240+$72.50= ($1050+$75)-($810+$42.50) $272.50 $1125-$852.50 $272.50

($1000+$5c+$15a)-($750+$6c+$8.50a) = $250-$1c+$6.50a ($1000+ $375+$1500)-($750+$450+$850) = $250-$75+$650 $2875- 2050=$325+$650 $825= $825 When you evaluate them it gives you the same answer, $825. The advantage is that it's quicker to calculate. The disadvantage is that you don't get to see the full working out of the problem as much.
 * 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?** Explain.
 * G.Compare the profit expressions you wrote in parts D and E. What are the advantages and disadvantages of writting profit expression in shorter form?**

__Follow-Up__

//**1.Benjamin's math test consisted of 10 questions, each wort 5 points. Benjamin answered 2 incorrectly.Show ate least two ways to clacuate his score.**// 5(10-2) or 8.5 are two ways to show Benjamins score on his math test were he got two of 10 questions wrong with each question being worth 5 points.

2. //**a) Describe a situation that can be represented by expressions 100-(x+y). Explain what x and y represent in the situation.**// A situation that could be represented by the expression 100-(x+y) could be the amount of juic boxes on the counter of a store with 100 being the amount of Juice boxes ,x being the amount of Juice boxes in the back ,and y being the amount of Juice boxes already sold.

//**b) Use the distributive property to help you write an expression that is equivalent to 100-(x+y)**// 100-x-y is equivalent to 100-(x+y).

3. //**a)Describe a situation that can be represented by the expression 50-2x-2y. Explain what x and y represent in your situation.**// 50-2x-2y could be the amount of Scary movies in the scary movie section of a movie rental, with x being the average amount of Scary movies on the bottom shelf, and y being the average amount of scary movies on the top of the shelf, and 50 being the amount of movies rented.

//**b: Use the distributive property to help you write an expression that is equivalent to 50-2x-2y.**// Using the distributive property an equivalent expression to 50-2x-2y could be 50-((2*x)+(2*y)).

//**4. The expression 3+2x is equivalent to 2x +3. Is 3-2x equivalent to 2x-3? Explain why or why not.**// No because while you can switch the position of terms around an addition sign you can’t change only part of a term.

//**5.Apply the properties you have learned in this investigation to simplify each expression.**// a. 7x+7 b. -2x-3 c. 5r+12t+38 d. 39-12x+9x