let t = mL water in tank
let p = mL water in the pail
Start with the first statement
t + p = 5136
Second statement
7(p - 314) = t + 314
Use substitution to re-write as one equation in one variable.
t = 5136 - p
7(p - 314) = 5136 - p + 314
7p - 2198 = 4822 - p
7p + p = 4822 + 2198
8p = 7020
p = 7020/8
p = 877.5 mL