1. **State the problem:** Solve the equation $32c + 5 = 24c + (c + 32)$ for $c$. 2. **Expand and simplify:** First, expand the right side: $$24c + (c + 32) = 24c + c + 32 = 25c + 32$$ So the equation becomes: $$32c + 5 = 25c + 32$$ 3. **Isolate variable terms:** Subtract $25c$ from both sides: $$32c + 5 - 25c = 25c + 32 - 25c$$ $$\cancel{32c} + 5 + \cancel{-25c} = \cancel{25c} + 32 + \cancel{-25c}$$ $$7c + 5 = 32$$ 4. **Isolate constant terms:** Subtract 5 from both sides: $$7c + 5 - 5 = 32 - 5$$ $$7c + \cancel{5} - \cancel{5} = 27$$ $$7c = 27$$ 5. **Solve for $c$:** Divide both sides by 7: $$\frac{7c}{7} = \frac{27}{7}$$ $$\cancel{7}c / \cancel{7} = \frac{27}{7}$$ $$c = \frac{27}{7}$$ **Final answer:** $$c = \frac{27}{7}$$