1. **Problem statement:** Kent receives successive discounts of 3% and 7% on a purchase of $850. (a) Calculate the price Kent pays. (b) Calculate what single percentage discount would be equivalent to the successive discounts. 2. **Step a - Calculate price after successive discounts:** - First discount is 3%, so price after first discount is $$850 \times (1 - 0.03) = 850 \times 0.97 = 824.5$$ - Second discount is 7%, so price after second discount is $$824.5 \times (1 - 0.07) = 824.5 \times 0.93 = 766.785$$ - Rounding to 2 decimal places, the price Kent pays is $$766.79$$ 3. **Step b - Calculate equivalent single discount:** - Let the equivalent discount be $$d$$. - The successive discount factor is $$0.97 \times 0.93 = 0.9021$$ - Therefore, $$1 - d = 0.9021 \implies d = 1 - 0.9021 = 0.0979 = 9.79\%$$ - The single equivalent percentage discount is $$9.79\%$$ 4. **Problem statement:** Carla earns a taxable income of $140000. Use the tax table to find her net income. 5. **Assuming the tax table has progressive tax brackets,** we calculate taxes and net income accordingly. (Since the tax table is not provided, I will assume an example tax rate for the purpose of explanation.) - For example, suppose tax is 30% flat rate (replace with actual tax table if given). - Tax paid = $$140000 \times 0.30 = 42000$$ - Net income = $$140000 - 42000 = 98000$$ If the actual tax table or rates are provided, please share them for an accurate calculation. **Final answers:** (a) Price Kent pays = $$766.79$$ (b) Equivalent single discount = $$9.79\%$$ (c) Carla's net income assuming 30% tax = $$98000$$