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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Let's break down the problem step by step to find out how many years it will take for Carlos to start earning money on his lemon tree.

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

2. **Annual Revenue**: Each year, the tree grows 7 lemons, and each lemon is sold for $1.5.
   - Revenue per year = 7 lemons * $1.5 per lemon = $10.5

3. **Annual Expenses**: It costs $3 per year to water and feed the tree.

4. **Net Profit per Year**: Subtract the annual expenses from the annual revenue.
   - Net profit per year = $10.5 - $3 = $7.5

5. **Break-even Point**: We need to find the number of years (let's call it \( n \)) it takes for the total net profit to cover the initial cost of $90.
   - Total net profit after \( n \) years = \( 7.5n \)
   - We set this equal to the initial cost: \( 7.5n = 90 \)

6. **Solving for \( n \)**:
   - \( n = \frac{90}{7.5} \)
   - \( n = 12 \)

So, it will take Carlos 12 years to start earning money on the lemon tree.

$\boxed{12}$