Question: Jerome has a lunch account at school. His account has a balance of $31.33. If Jerome spends $4.19 each day for lunch and no additional money is deposited to his account, how many days can he eat lunch until his account balance is negative? Simplify your answer completely and enter your answer as a whole number.
1. **State the problem:** Jerome starts with a balance of $31.33 and spends $4.19 each day. We want to find how many whole days he can spend $4.19 before his balance becomes negative.
2. **Set up the inequality:** Let $d$ be the number of days Jerome can eat lunch.
We want the balance to be non-negative:
$$31.33 - 4.19d \geq 0$$
3. **Solve the inequality:**
$$31.33 \geq 4.19d$$
Divide both sides by $4.19$:
$$\frac{31.33}{\cancel{4.19}} \geq d \quad \Rightarrow \quad d \leq \frac{31.33}{4.19}$$
Calculate the division:
$$d \leq 7.48$$
4. **Interpret the result:** Since $d$ must be a whole number of days and Jerome cannot spend a partial day, he can eat lunch for at most $7$ full days before the balance becomes negative.
**Final answer:**
$$\boxed{7}$$