$w=6+\frac{3 x y}{75}$ $\newline$ 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 $x$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\frac{25 w}{x}-6$ $\newline$ (B) $y=\frac{25 w+150}{x}$ $\newline$ (C) $y=\frac{25 w-150}{x}$ $\newline$ (D) $y=\frac{25 w-2}{x}$

Full solution

w=6+\frac{3 x y}{75}

\newline

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

\newline

Choose

1

answer:

\newline

(A)

y=\frac{25 w}{x}-6

\newline

(B)

y=\frac{25 w+150}{x}

\newline

(C)

y=\frac{25 w-150}{x}

\newline

(D)

y=\frac{25 w-2}{x}

Given Equation: We start with the given equation: $\newline$ $w = 6 + \frac{3xy}{75}$ $\newline$ 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: $\newline$ $w - 6 = \frac{3xy}{75}$
Eliminate Denominator: Next, we multiply both sides of the equation by $75$ to eliminate the denominator: $75(w - 6) = 3xy$
Solve for y: Now, we divide both sides of the equation by $3x$ to solve for y: $\newline$ $\frac{75(w - 6)}{3x} = y$
Simplify Equation: We simplify the equation by distributing $75$ and dividing by $3x$ : $y = \frac{(75w - 450)}{(3x)}$
Final Expression: Further simplification gives us: $\newline$ $y = \frac{25w - 150}{x}$
Compare with Answer Choices: We compare the simplified expression for $y$ with the answer choices provided: $\newline$ (A) $y = \frac{25w}{x} - 6$ (Incorrect, as it does not match our expression) $\newline$ (B) $y = \frac{25w + 150}{x}$ (Incorrect, as it does not match our expression) $\newline$ (C) $y = \frac{25w - 150}{x}$ (Correct, as it matches our expression) $\newline$ (D) $y = \frac{25w - 2}{x}$ (Incorrect, as it does not match our expression)