The given equation to represent the litter collection situation is incorrect, and as such, we cannot determine the accurate number of pieces collected by each person. Therefore, all the provided statements about the number of pieces collected by the volunteers Sara and Dominique, as well as the value of x, are false.
Step-by-step explanation:
Let's analyze each statement given about the litter collection situation. The variables used are as follows: Let x represent the number of pieces of litter Vaughn collected, P represent the number of pieces Piper collected, S represent the number of pieces Sara collected, and D represent the number of pieces Dominique collected.
Equation representation: The first statement gives us the equation x = 9(S + P + D). However, with the additional information provided, we can simplify it as follows:
Sara collected 12 more pieces of litter than Piper (S = P + 12), Piper and Vaughn collected the same amount (P = x), and Dominique collected 15 fewer pieces than Sara (D = S - 15). Substituting these variables, we get: x = 9(P + P + 12 + P - 15), which simplifies to x = 9(3P - 3). Since P = x, the equation becomes x = 9(3x - 3). This equation is incorrect, so the first statement is False.
x=18: Since the provided equation is incorrect, we cannot determine the value of x from it. Therefore, without additional correct information, we cannot assert whether x equals 18, so the statement is False.
Sara collected 30 pieces of litter: We cannot confirm this as we do not have a correct equation that gives us the values for how much Sara collected. Hence, this statement is False.
Dominique collected 45 pieces of litter: Again, without a correct equation, we cannot determine how many pieces Dominique collected. This statement is therefore False.