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 me work through this step by step.

First, let me identify the key information:
- Initial planting cost: $90
- Each year: 7 lemons produced, each sold for $1.50
- Each year: $3 cost to water and feed the tree

Let me calculate the net profit per year:
- Revenue per year = 7 lemons × $1.50 per lemon = $10.50
- Expenses per year = $3
- Net profit per year = $10.50 - $3 = $7.50

Now I need to find when the cumulative profit exceeds the initial investment.

Let's say it takes n years to break even:
- Total revenue after n years = n × $10.50
- Total expenses after n years = $90 (initial) + n × $3
- Net profit after n years = n × $10.50 - ($90 + n × $3)
- Net profit after n years = n × $10.50 - $90 - n × $3
- Net profit after n years = n × ($10.50 - $3) - $90
- Net profit after n years = n × $7.50 - $90

To find when he starts earning money, I need the net profit to be positive:
n × $7.50 - $90 > 0
n × $7.50 > $90
n > $90/$7.50
n > 12

Since n must be a whole number of years, and we want the first year when he starts earning money (when profit becomes positive), this happens in year 13.

Let me verify:
- After 12 years: Profit = 12 × $7.50 - $90 = $90 - $90 = $0 (break-even)
- After 13 years: Profit = 13 × $7.50 - $90 = $97.50 - $90 = $7.50 (positive profit)

Therefore, it takes 13 years before he starts earning money on the lemon tree.

\boxed{13}