Let's break down the information given step by step to find out how much money Rama had at the beginning.
First, Rama bought some textbooks with $8 more than 1/3 of his money. Let's say the amount of money he spent on textbooks is represented by x. We can set up the equation:
x = (1/3)m + 8
Next, Rama bought his stationery with $12.20 less than 1/2 of his remaining money. After buying the textbooks, he had (m - x) money left, where m represents the initial amount of money he had. We can set up the equation:
(m - x) / 2 = x - 12.20
Lastly, Rama bought some school socks with $2.80 more than 1/2 of the money left. After buying the stationery, he had ((m - x) - (x - 12.20)) money left. We can set up the equation:
((m - x) - (x - 12.20)) = (1/2)((m - x) - (x - 12.20)) + 2.80
Given that Rama had $15.40 with him after all the purchases, we can solve these equations to find the initial amount of money he had. However, it would be helpful to know the values of x, (m - x), and ((m - x) - (x - 12.20)) to proceed with the calculations. Could you provide those values?