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 need to calculate the total costs and the total earnings for each year and find the point at which earnings exceed costs.

1. Initial cost to plant the tree: $90
2. Annual cost to water and feed the tree: $3
3. Annual earnings from selling lemons: 7 lemons * $1.5 per lemon = $10.5

We need to find the number of years (n) it will take for the total earnings to exceed the total costs.

Total cost after n years = Initial cost + (Annual cost * n)
Total earnings after n years = Annual earnings * n

We need to find the smallest n such that:
Annual earnings * n > Initial cost + (Annual cost * n)

Let's set up the inequality:
10.5n > 90 + 3n

Subtract 3n from both sides:
7.5n > 90

Divide both sides by 7.5:
n > 12

Since n must be a whole number, Carlos will start earning money after 13 years.

Final answer: \boxed{13}