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The residents of Kamrupa spend all of their income on cauliflower, broccoli, and carrots. In 2022, they buy 100 heads of cauliflower for $200, 50 bunches of broccoli for $75, and 500 carrots for $50. In 2023, they buy 75 heads of cauliflower for $225, 80 bunches of broccoli for $129, and 500 carrots for $100.

a) Calculate the price of each vegetable in each year.

b) Using 2022 as the base year, calculate the CPI for each year.

c) What is the inflation rate in 2023?

Please explain in detail