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Value After First Week: p - 15 The value of the stock tripled the next week. In other words, during the second week, the value of Kevin's investment is three times the value at the first week. Value After First Week:& p - 15 Value After Second Week:& 3(p - 15) If the value of the investment grows by $35 during the last week, it will be $35 more than the value after the second week. Value After First Week:& p - 15 Value After Second Week:& 3(p - 15) Value After Third Week:& 3(p - 15)+35 The final value of Kevin's investment would be $140, which will complete the equation. 3 (p-15) + 35= 140

3 (p-15) +35= 140 First, apply the Distributive Property to clear the parentheses. Then, apply the Properties of Equality to isolate the variable p. The solution to the equation from Part A is p = 50. This means that Kevin invested $50.

Value of Tearrik's Investment: 2(m-10) The value of Ramsha's investment grew by a third during the first week, so its value after the first week was 1m+ 13m= 43m. During the second week, the value grew by $10. Then, the value of Ramsha's investment after two weeks is 43m+10. Value of Ramsha's Investment: 4/3m+10 Since the final values of Tearrik's and Ramsha's investments are equal, an equation can be written by setting these two expressions equal to each other. 2(m-10) = 4/3m+10

2(m-10) = 4/3m+10 First, use the Distributive Property. The resulting equation has variable terms on both sides. To solve the equation, all the variable terms are first collected on one side of the equation. Use the Subtraction Property of Equality to subtract 43m from both sides. Finally, isolate the variable using inverse operations and the Properties of Equality. The solution to the equation from Part A is m = 45. This means that Tearrik and Ramsha invested $45 each in their stocks.

Value of Tiffaniqua's Investment: 2/3t+20 The value of Zosia's investment grew by $30 during the first week, so its value was t+30 at that point. Then the value fell by a third during the second week. This means that the value of Zosia's investment after two weeks is 23(t+30). Value of Zosia's Investment: 2/3(t+30) The values of Tiffaniqua's and Zosia's investments after two weeks are equal. This makes it possible to write an equation that models the given situation. 2/3t+20 = 2/3(t+30)

First Stock: 2(g-10) The second stock doubled its value during the first week, so the value would be 2g at that point. In the second week, the value would grow by $15, so the final value is 2g+15. Second Stock: 2g+15 Ali wants to know how much money invested into both stocks would result in the final values being equal. The best way to find this information is to set the two expressions equal to each other. 2(g-10)=2g+15

• If solving the equation results in a false statement, the equation has no solutions.
• If solving the equation results in a solution, the equation has one solution.
• If solving the equation results in an identity, the equation has infinitely many solution.

First, solve the equation from Part A. The first step is to use the Distributive Property. Solving the equation resulted in an identity, which means that every number is a solution to the equation. No matter how much Tiffaniqua and Zosia invested in their stocks, the values of both investments would be equal after two weeks. Next, solve the equation written in Part B, starting again with the Distributive Property. The next step is to collect all the variable terms on one side and combine like terms. In this case, use the Subtraction Property of Equality to subtract 2g from both sides of the equation. This is a false statement, so this equation has no solutions. In other words, no amount of money invested in the two stocks would result in both investments having the same value after two weeks. The following statements are true.

• The equation from Part A has infinitely many solutions.
• The equation from Part B has no solutions.

Starting Amount of Money: w Next, the final value of Tiffaniqua's stock can be expressed in terms of w.

• After the first week, Tiffaniqua's investment was worth $65 more, or w+65.
• During the second week, the stock value doubled, so the investment was worth 2(w+65) at this point.
• During the last week of the project, the value of the stock fell by $50, making the final value 2(w+65)-50.

The following expression represents final value of Tiffaniqua's stock. Final Value: 2(w+65)-50 Finally, write the equation by setting this expression equal to the final value of the investment, $280. 2(w+65)-50 = 280

2(w+65)-50 = 280 Start by analyzing the expression. Here, 65 is added to w and the result is then multiplied by 2. Finally, 50 is subtracted from the product. These operations can be undone using inverse operations. The first operation to be undone is the subtraction. Use the Addition Property of Inequality to undo the subtraction. Then, the multiplication is undone using the Division Property of Equality. Finally, use the Subtraction Property of Equality to undo the addition. The solution to the equation is w = 100. This means that Tiffaniqua started the simulated stock market project with $100.