1. **Stating the problem:** We have two equations based on the amounts of money made by selling items priced at $x$ and $y$ dollars. Given: $$9x + 2y = 36.05$$ $$7y + 5x = 48$$ We need to find the values of $x$ and $y$. 2. **Formula and approach:** This is a system of linear equations. We can solve it using substitution or elimination. 3. **Step 1: Rearrange the first equation to express $y$ in terms of $x$:** $$9x + 2y = 36.05 \implies 2y = 36.05 - 9x \implies y = \frac{36.05 - 9x}{2}$$ 4. **Step 2: Substitute $y$ into the second equation:** $$7y + 5x = 48$$ Substitute $y$: $$7 \times \frac{36.05 - 9x}{2} + 5x = 48$$ 5. **Step 3: Simplify and solve for $x$:** $$\frac{7}{2}(36.05 - 9x) + 5x = 48$$ $$\frac{7}{2} \times 36.05 - \frac{7}{2} \times 9x + 5x = 48$$ $$126.175 - 31.5x + 5x = 48$$ $$126.175 - 26.5x = 48$$ 6. **Step 4: Isolate $x$:** $$-26.5x = 48 - 126.175$$ $$-26.5x = -78.175$$ $$x = \frac{-78.175}{-26.5} = 2.95$$ 7. **Step 5: Substitute $x$ back to find $y$:** $$y = \frac{36.05 - 9 \times 2.95}{2} = \frac{36.05 - 26.55}{2} = \frac{9.5}{2} = 4.75$$ **Final answer:** $$x = 2.95, \quad y = 4.75$$ These are the prices of the items corresponding to $x$ and $y$.