Answer: B. $t+c=36$, $0.55t+0.75c=25$

Explanation:1. Understand the problem: Let $t$ be the original price of the towel in dollars. Let $c$ be the original price of the chair in dollars. The combined original price for the towel and chair is $$36$. The towel has a $45\%$ discount. The chair has a $25\%$ discount. The combined sale price for the two items is $$25$. We need to find the system of equations that represents this situation.

2. Formulate the first equation based on the combined original price: The sum of the original prices is $$36$: $t + c = 36$

3. Formulate the second equation based on the combined sale price: - Discount on the towel is $45\%$. So, the sale price of the towel is $100\% - 45\% = 55\%$ of its original price, which is $0.55t$. - Discount on the chair is $25\%$. So, the sale price of the chair is $100\% - 25\% = 75\%$ of its original price, which is $0.75c$. The combined sale price is $$25$: $0.55t + 0.75c = 25$

4. Combine the two equations to form the system: Equation 1: $t + c = 36$ Equation 2: $0.55t + 0.75c = 25$

5. Compare with the given options: [A] $t+c=36$, $0.45t+0.25c=25$ (Incorrect: uses discount amounts instead of sale price percentages for the second equation's coefficients) [B] $t+c=36$, $0.55t+0.75c=25$ (Correct) [C] $t+c=36$, $0.25t+0.45c=25$ (Incorrect: swapped discount percentages) [D] $t+c=36$, $0.75t+0.55c=25$ (Incorrect: swapped sale price percentages)

6. Conclusion: The system of equations that gives the original price $t$ of the towel and $c$ of the chair is: $t+c=36$ $0.55t+0.75c=25$ This matches option [B].