1. **State the problem:** Ben buys 10 books. The first book costs 3. Each subsequent book doubles in price. After the 6th book, each additional book gets a 15% discount. 2. **Define the prices:** - Price of 1st book: $3$ - Price of 2nd book: $3 \times 2 = 6$ - Price of 3rd book: $6 \times 2 = 12$ - Price of 4th book: $12 \times 2 = 24$ - Price of 5th book: $24 \times 2 = 48$ - Price of 6th book: $48 \times 2 = 96$ 3. **Calculate prices for books 7 to 10 with 15% discount:** - Price before discount doubles each time: - 7th book: $96 \times 2 = 192$ - 8th book: $192 \times 2 = 384$ - 9th book: $384 \times 2 = 768$ - 10th book: $768 \times 2 = 1536$ - Apply 15% discount means paying 85% of the price: - 7th book: $192 \times 0.85 = 163.2$ - 8th book: $384 \times 0.85 = 326.4$ - 9th book: $768 \times 0.85 = 652.8$ - 10th book: $1536 \times 0.85 = 1305.6$ 4. **Sum all prices:** - Sum of first 6 books: $3 + 6 + 12 + 24 + 48 + 96 = 189$ - Sum of last 4 books: $163.2 + 326.4 + 652.8 + 1305.6 = 2448$ 5. **Total cost:** $$189 + 2448 = 2637$$ **Answer:** Ben pays a total of 2637 for all 10 books.