1. **State the problem:** Ethan wants to bake cupcakes. Each batch requires $1 \frac{2}{3}$ cups of sugar. He has 15 cups but must save $\frac{2}{3}$ cup for his wife. How many batches can he make? 2. **Define the variable:** Let $x$ be the number of batches Ethan can make. 3. **Write the equation:** Total sugar available for baking is $15 - \frac{2}{3}$ cups. Each batch requires $1 \frac{2}{3} = \frac{5}{3}$ cups. So, the equation is: $$\frac{5}{3}x = 15 - \frac{2}{3}$$ 4. **Solve the equation:** Calculate the sugar available: $$15 - \frac{2}{3} = \frac{45}{3} - \frac{2}{3} = \frac{43}{3}$$ So, $$\frac{5}{3}x = \frac{43}{3}$$ Multiply both sides by $\cancel{\frac{3}{5}} \times \frac{3}{3}$ to isolate $x$: $$x = \frac{43}{3} \times \frac{3}{5} = \frac{43}{\cancel{3}} \times \frac{\cancel{3}}{5} = \frac{43}{5}$$ Simplify: $$x = 8.6$$ 5. **Explain the meaning:** Ethan can make 8 full batches of cupcakes because he cannot make a partial batch with the sugar available. 6. **Does the solution make sense?** Yes, it makes sense because the number of batches must be a whole number or less than the total sugar allows. 8 full batches can be made with some sugar left over but not enough for a 9th batch.