1. **State the problem:** Solve the system of equations: $$7.5a + 4b + 3.5c = 3025$$ $$3b + c = 500$$ 2. **Identify the goal:** We want to find values of $a$, $b$, and $c$ that satisfy both equations. 3. **Use substitution or elimination:** From the second equation, express $c$ in terms of $b$: $$c = 500 - 3b$$ 4. **Substitute $c$ into the first equation:** $$7.5a + 4b + 3.5(500 - 3b) = 3025$$ 5. **Simplify the equation:** $$7.5a + 4b + 1750 - 10.5b = 3025$$ 6. **Combine like terms:** $$7.5a + (4b - 10.5b) + 1750 = 3025$$ $$7.5a - 6.5b + 1750 = 3025$$ 7. **Isolate terms:** $$7.5a - 6.5b = 3025 - 1750$$ $$7.5a - 6.5b = 1275$$ 8. **Express $a$ in terms of $b$:** $$7.5a = 1275 + 6.5b$$ $$a = \frac{1275 + 6.5b}{7.5}$$ **Summary:** - $c = 500 - 3b$ - $a = \frac{1275 + 6.5b}{7.5}$ Since there are two equations and three variables, the system has infinitely many solutions depending on $b$. You can choose any value for $b$ and find corresponding $a$ and $c$.