Let's represent the initial amount of money each person had as follows:
Raju = R
Sam = S
Tristan = T
We know that:
R + S + T = 435
Raju spent 4/5 of his money, so he has 1/5 of his money left:
R = (1/5)R
Sam spent 2/3 of his money, so he has 1/3 of his money left:
S = (1/3)S
Tristan spent 3/4 of his money, so he has 1/4 of his money left:
T = (1/4)T
We also know that Raju has $55 more than Sam:
R = S + 55
And Tristan has $10 more than Sam:
T = S + 10
Now, we can substitute the expressions for R, S, and T into the total money equation:
(1/5)R + (1/3)S + (1/4)T = 435
Substitute R = S + 55 and T = S + 10 into the equation above:
(1/5)(S + 55) + (1/3)S + (1/4)(S + 10) = 435
Solving the equation above gives:
S = 180
Now that we have found the value of S, we can find the amount of money Tristan had at first:
T = S + 10
T = 180 + 10
T = 190
Therefore, Tristan originally had $190.
