Final answer:
The student had at least $50 in their bank account initially to meet the condition of having at least $34 left after spending $16.
Step-by-step explanation:
If a student had d dollars in their bank account and they spent $16 but still have at least $34 left, we can set up the following inequality to determine how much they initially had:
d - 16 ≥ 34
By adding 16 to both sides of the inequality, we get:
d ≥ 34 + 16
d ≥ 50
Therefore, the student must have had at least $50 initially in their bank account to have at least $34 after spending $16.