Final answer:
After calculating the two successive discounts of 15% and 5% on the initial price of the television and then subtracting the $50 mail-in rebate, the final amount Rachel will pay is $2372.50.
Step-by-step explanation:
To find the final amount Rachel will pay for the television, we need to calculate the successive discounts of 15% and 5% on the initial price, and then subtract the $50 mail-in rebate.
After calculating the two successive discounts of 15% and 5% on the initial price of the television and then subtracting the $50 mail-in rebate, the final amount Rachel will pay is $2372.50.
First discount (15% off): $3000 × 0.15 = $450.
Sale price after first discount: $3000 - $450 = $2550.
Second discount (5% off the sale price): $2550 × 0.05 = $127.50.
Sale price after second discount: $2550 - $127.50 = $2422.50.
Final amount after mail-in rebate: $2422.50 - $50 = $2372.50.
Therefore, the final amount Rachel will pay for the television is $2372.50, which corresponds to option (b).