Question: Cory is buying a new home theater for his apartment. The system costs $3800$, and he can take it home if he puts $1000$ down and makes $6$ interest-free payments over $6$ months.
How much will Cory have to pay with each payment?
1. **State the problem:** Cory wants to buy a home theater costing $3800$. He pays $1000$ down and then makes $6$ equal interest-free payments.
2. **Find the remaining balance after the down payment:**
$$3800 - 1000 = 2800$$
3. **Calculate each payment by dividing the remaining balance by the number of payments:**
$$\frac{2800}{6}$$
4. **Simplify the fraction:**
$$\frac{2800}{6} = \frac{\cancel{2800}^{\div 2} 1400}{\cancel{6}^{\div 2} 3} = \frac{1400}{3}$$
5. **Convert to decimal:**
$$\frac{1400}{3} = 466.66\overline{6}$$
6. **Answer:** Cory will have to pay approximately $466.66$ with each payment.