Rob begins with R cents, Sam begins with S cents.
Rob has twice as much as Sam.
R = 2S
Then Sam gives Rob 1 quarter, 2 nickels, and 3 pennies.
(That's 38 cents)
Now Sam has S-38 cents, and Rob has R+38
Rob then gives Sam 8 dimes.
(That's 80 cents)
Now Sam has S-38+80, and Rob has R+38-80.
Simplifying,
Now Sam has S+42 cents and Rob has R-42
...they both end up with the same amount.
(set them equal)
So S+42 = R-42
S = R-84
So we have this system of equations to solve:
R = 2S
S = R-84
Solve that system by substitution and get
R = 168 cents or $1.68, S = 84 cents.
Rob originally had $1.68
Edwin