Last month, the price of one pound of carrots was \( \$ 2 \frac{1}{5} \) and Joe sold \( 12 \frac{1}{12} \) pounds of carrots. This month, the price has increased by \( \$ 1 \frac{1}{10} \) and Farmer Joe only sold. \( 5 \frac{1}{8} \) pounds of carrots. What is the price of a pound of carrots this month?

To find the price of a pound of carrots this month, we first need to convert the mixed numbers to improper fractions. The price of one pound of carrots last month was \( \$ 2 \frac{1}{5} \). Converting this to an improper fraction: \[ 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} \] This month, the price increased by \( \$ 1 \frac{1}{10} \). Converting this to an improper fraction: \[ 1 \frac{1}{10} = \frac{1 \times 10 + 1}{10} = \frac{10 + 1}{10} = \frac{11}{10} \] Now, we add the increase in price to last month's price: \[ \text{New Price} = \frac{11}{5} + \frac{11}{10} \] To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10: \[ \frac{11}{5} = \frac{11 \times 2}{5 \times 2} = \frac{22}{10} \] Now we add: \[ \frac{22}{10} + \frac{11}{10} = \frac{22 + 11}{10} = \frac{33}{10} \] Finally, converting \( \frac{33}{10} \) back to a mixed number: \[ 33 \div 10 = 3 \quad \text{remainder } 3 \quad \Rightarrow \quad 3 \frac{3}{10} \] Thus, the price of a pound of carrots this month is \( \$ 3 \frac{3}{10} \).