Answer :
First, convert the mixed numbers into improper fractions.
1. The first week's nails weigh
$$40\frac{1}{10} = 40 + \frac{1}{10} = \frac{40 \times 10 + 1}{10} = \frac{401}{10}.$$
2. The multiplier for the second week is
$$2\frac{1}{2} = 2 + \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}.$$
Next, multiply the weight from the first week by the multiplier:
$$
\frac{401}{10} \times \frac{5}{2} = \frac{401 \times 5}{10 \times 2} = \frac{2005}{20}.
$$
Now, simplify the fraction:
$$
\frac{2005}{20} = \frac{2005 \div 5}{20 \div 5} = \frac{401}{4}.
$$
To express $\frac{401}{4}$ as a mixed number, divide 401 by 4:
- The quotient is 100, because $100 \times 4 = 400$.
- The remainder is $401 - 400 = 1$.
Thus,
$$
\frac{401}{4} = 100\frac{1}{4}.
$$
So, the construction worker bought
$$\boxed{100\frac{1}{4}\ \text{lb}}$$
of nails in the second week.
1. The first week's nails weigh
$$40\frac{1}{10} = 40 + \frac{1}{10} = \frac{40 \times 10 + 1}{10} = \frac{401}{10}.$$
2. The multiplier for the second week is
$$2\frac{1}{2} = 2 + \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}.$$
Next, multiply the weight from the first week by the multiplier:
$$
\frac{401}{10} \times \frac{5}{2} = \frac{401 \times 5}{10 \times 2} = \frac{2005}{20}.
$$
Now, simplify the fraction:
$$
\frac{2005}{20} = \frac{2005 \div 5}{20 \div 5} = \frac{401}{4}.
$$
To express $\frac{401}{4}$ as a mixed number, divide 401 by 4:
- The quotient is 100, because $100 \times 4 = 400$.
- The remainder is $401 - 400 = 1$.
Thus,
$$
\frac{401}{4} = 100\frac{1}{4}.
$$
So, the construction worker bought
$$\boxed{100\frac{1}{4}\ \text{lb}}$$
of nails in the second week.
