1. **State the problem:** We are given the linear equation $$Y = 52.50 - 0.85X$$ and asked to find the value of $X$ when $Y=6$ and when $Y=4$. 2. **Formula and approach:** To find $X$, we rearrange the equation to solve for $X$: $$Y = 52.50 - 0.85X \implies 0.85X = 52.50 - Y \implies X = \frac{52.50 - Y}{0.85}$$ 3. **Find $X$ when $Y=6$:** $$X = \frac{52.50 - 6}{0.85} = \frac{46.50}{0.85}$$ 4. **Simplify the fraction:** $$X = \frac{46.50}{0.85} = 54.7058823529 \approx 54.71$$ 5. **Find $X$ when $Y=4$:** $$X = \frac{52.50 - 4}{0.85} = \frac{48.50}{0.85}$$ 6. **Simplify the fraction:** $$X = \frac{48.50}{0.85} = 57.0588235294 \approx 57.06$$ **Final answers:** - When $Y=6$, $X \approx 54.71$ - When $Y=4$, $X \approx 57.06$