Under his cell phone plan, Elijah pays a flat cost of $46.50 per month and $4 per gigabyte. He wants to keep his bill at $58.50 per month. How many gigabytes of data can he use while staying within his budget?
Let x be the number of gigabytes Elijah uses.
His monthly bill will be x*$4 + $46.50.
Setting this expression equal to his desired total, we get x*$4 + $46.50 = $58.50.
Subtracting $46.50 from both sides, we get x*$4 = $12.
Dividing both sides by $4, we get x = 3.
Thus, Elijah can use up to 3 gigabytes. Answer: \boxed{3}.