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# Need help

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Raju, Sam, and Tristan had 435\$. Raju spent 4/5 of his money. Sam spent 2/3 of his money and Tristan spent 3/4 of his money. In the end, Raju has 55\$ more than Sam. Tristan has \$10 more than Sam. How much money Tristan has at first?

Jul 4, 2024

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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