Solve for minimum x value in two-variable equation provided a ratio

Question

The equation is:

$$500 = 5x - 2y$$

I know the ratio of x to y is $7:3$; what is the minimum possible value of x and how would I approach this question?

Answer 1

You can set up two equations $$500=5x-2y\\\frac{x}{y}=\frac{7}{3}\text{ or }y=\frac{3x}{7}$$

Knowing that $y=\frac{3x}{7}$, you can sub that into the other equation $$500=5x-2\frac{3x}{7}=5x-\frac{6}{7}x$$ and solve for x.