Subjects algebra

Solve Equation B8169D

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Solve Equation B8169D


1. **State the problem:** Solve the equation $$30000x + 67500y + 30000xy = 39375$$ for one variable in terms of the other. 2. **Rewrite the equation:** Group terms involving $x$: $$30000x + 30000xy + 67500y = 39375$$ 3. **Factor $x$ out of terms where it appears:** $$30000x(1 + y) + 67500y = 39375$$ 4. **Isolate the term with $x$:** $$30000x(1 + y) = 39375 - 67500y$$ 5. **Solve for $x$:** $$x = \frac{39375 - 67500y}{30000(1 + y)}$$ 6. **Simplify the fraction:** Divide numerator and denominator by 375: $$x = \frac{105 - 180y}{80(1 + y)}$$ 7. **Final expression:** $$\boxed{x = \frac{105 - 180y}{80(1 + y)}}$$ This expresses $x$ in terms of $y$. You can substitute any value of $y \neq -1$ to find $x$.