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}.

<!-- imported from openai/gsm8k (test) -->

To find out how many years it will take for Carlos to start earning money on the lemon tree, we need to calculate when the total profit from the tree equals or exceeds the initial cost of planting it.

**Step 1: Calculate the annual revenue from selling lemons.**
Carlos grows 7 lemons each year and sells them for $1.5 each.
$$ \text{Annual Revenue} = 7 \text{ lemons} \times \$1.5/\text{lemon} = \$10.50 $$

**Step 2: Calculate the annual net profit.**
Each year, it costs $3 to water and feed the tree. We subtract this cost from the annual revenue to find the net profit per year.
$$ \text{Annual Net Profit} = \text{Annual Revenue} - \text{Annual Cost} $$
$$ \text{Annual Net Profit} = \$10.50 - \$3.00 = \$7.50 $$

**Step 3: Calculate the number of years to recover the initial cost.**
The initial cost to plant the tree is $90. We need to find how many years ($n$) of net profit are required to cover this cost.
$$ n \times \$7.50 = \$90 $$
$$ n = \frac{90}{7.50} $$

To solve the division:
$$ \frac{90}{7.5} = \frac{900}{75} $$
Dividing both numerator and denominator by 25:
$$ \frac{900 \div 25}{75 \div 25} = \frac{36}{3} = 12 $$

So, it takes 12 years for the tree to generate enough net profit to cover the initial $90 cost. After 12 years, Carlos has broken even, and any profit generated thereafter is money he starts "earning" on the tree.

\boxed{12}