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 can be sold for $1.5. So, the annual revenue from selling lemons is:
   \[
   7 \text{ lemons} \times \$1.5 \text{ per lemon} = \$10.5
   \]

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

4. **Net Annual Profit**: The net profit each year is the annual revenue minus the annual cost:
   \[
   \$10.5 \text{ (revenue)} - \$3 \text{ (cost)} = \$7.5 \text{ per year}
   \]

5. **Break-even Point**: To find out how many years it will take to cover the initial cost of $90, we divide the initial cost by the net annual profit:
   \[
   \frac{\$90}{\$7.5 \text{ per year}} = 12 \text{ years}
   \]

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

$\boxed{12}$