w=6+(3xy)/(75) The equation gives the quantity w in terms of the quantities x and y. Which of the following equations correctly expresses y in terms of w and x ? Choose 1 answer: (A) y=(25 w)/(x)-6 (B) y=(25 w+150)/(x) (C) y=(25 w-150)/(x) (D) y=(25 w-2)/(x)

Question

w=6+(3xy)/(75) The equation gives the quantity  w in terms of the quantities  x and  y. Which of the following equations correctly expresses  y in terms of  w and  x ? Choose 1 answer: (A)  y=(25 w)/(x)-6 (B)  y=(25 w+150)/(x) (C)  y=(25 w-150)/(x) (D)  y=(25 w-2)/(x)

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Given Equation: We start with the given equation: w = 6 + (3xy) / 75 Our goal is to solve for y in terms of w and x.Isolate Term with y: First, we isolate the term containing y on one side of the equation by subtracting 6 from both sides: w - 6 = (3xy) / 75Eliminate Denominator: Next, we multiply both sides of the equation by 75 to eliminate the denominator: 75(w - 6) = 3xySolve for y: Now, we divide both sides of the equation by 3x to solve for y: (75(w - 6)) / (3x) = ySimplify Equation: We simplify the equation by distributing 75 and dividing by 3x: y = (75w - 450) / (3x)Final Expression: Further simplification gives us: y = (25w - 150) / xCompare with Answer Choices: We compare the simplified expression for y with the answer choices provided: (A) y = (25w) / x - 6 (Incorrect, as it does not match our expression) (B) y = (25w + 150) / x (Incorrect, as it does not match our expression) (C) y = (25w - 150) / x (Correct, as it matches our expression) (D) y = (25w - 2) / x (Incorrect, as it does not match our expression)

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