gsm8k-0012

# GSM8K Problem 13

Carlos is planting a lemon tree. The tree will cost $90 to plant. Each year it will grow 7 lemons, which he can sell for $1.5 each. It costs $3 a year to water and feed the tree. How many years will it take before he starts earning money on the lemon tree?

Reason step by step, then give ONLY the final answer on the last line as \boxed{ANSWER}.

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To determine how many years it will take for Carlos to start earning money on the lemon tree, we'll analyze the costs and revenues over time.

1. **Initial Cost:**
   - The tree costs $90 to plant initially.

2. **Annual Revenue:**
   - Each year, the tree produces 7 lemons.
   - Each lemon sells for $1.5.
   - Annual revenue from selling lemons: \(7 \times 1.5 = 10.5\) dollars.

3. **Annual Costs:**
   - It costs $3 per year to water and feed the tree.
   - Net annual profit: \(10.5 - 3 = 7.5\) dollars.

4. **Break-even Point:**
   - We need to find the smallest integer \(n\) such that the cumulative profit covers the initial cost.
   - Cumulative profit after \(n\) years: \(7.5 \times n\).
   - Set \(7.5 \times n \geq 90\).
   - Solve for \(n\): \(n \geq \frac{90}{7.5} = 12\).

5. **Verification:**
   - After 12 years, cumulative profit: \(7.5 \times 12 = 90\) dollars.
   - This exactly covers the initial cost, so Carlos starts earning money at the end of the 12th year.

\[
\boxed{12}
\]