Phil solved the equation x + 235.12 = 310.21, and found the solution to be 545.33. Is he correct? If not, what was his mistake?

He is not correct

x + 235.12 = 310.21 to solve this you must subtract 235.12 from each side

-235.12 - 235.12

x = 75.09

it appears he added instead of subtracting

No. He added 235.12 and 310.21, whereas he should have subtracted 235.12 from 310.21.

Step-by-step explanation:

First note that the "jump" from 235 (approx.) to 310 (approx) could not possibly be 545 (approx.) Looks like Phil added together 235 and 310, whereas he should have subtracted 235 from 310. Doing so now yields 75 (approx).

For the purpose of answering this question, rounded off numbers are perfectly adequate. If an "exact" answer is wanted, then subtract 235.12 from 310.21; the result should be 75.09 (which is only 0.09 off from my estimate).