Data
rate 1 = 11%
rate 2 = 14%
account 1 = y
account 2 = y + 550
total interest = $102
total interest = account 1 x rate 1 / 100 + account 2 x rate 2/ 100
Substitution
102 = (y x 11)/100 + [(y+550) x 14]/100
Solve for y
102 = 0.11y + 0.14y + 77.77
102 - 77.77 = 0.25y
24.23 = 0.25y
y = 24.23/0.25
y = 96.92
account 1 has $96.92
account 2 has $96.92 + $500 = $596.92