Answer :
First, express the numbers as improper fractions:
1. The nails purchased in the first week are
$$40 \frac{1}{10} = \frac{40 \times 10 + 1}{10} = \frac{401}{10}.$$
2. The multiplier of the nails purchased in the second week is
$$2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}.$$
Next, multiply the first week's amount by the multiplier to find the pounds of nails bought in the second week:
$$\text{Second week nails} = \frac{401}{10} \times \frac{5}{2} = \frac{401 \times 5}{10 \times 2} = \frac{2005}{20}.$$
Simplify the fraction by dividing by 5 (or by noticing that dividing numerator and denominator by their common factor):
$$\frac{2005}{20} = \frac{401}{4}.$$
Now, convert the improper fraction $\frac{401}{4}$ into a mixed number. Divide 401 by 4:
- The quotient is 100 since $4 \times 100 = 400$.
- The remainder is 1, giving the fraction $\frac{1}{4}$.
Thus, the final answer is
$$100 \frac{1}{4} \text{ pounds}.$$
The construction worker bought $100 \frac{1}{4}$ pounds of nails in the second week.
1. The nails purchased in the first week are
$$40 \frac{1}{10} = \frac{40 \times 10 + 1}{10} = \frac{401}{10}.$$
2. The multiplier of the nails purchased in the second week is
$$2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}.$$
Next, multiply the first week's amount by the multiplier to find the pounds of nails bought in the second week:
$$\text{Second week nails} = \frac{401}{10} \times \frac{5}{2} = \frac{401 \times 5}{10 \times 2} = \frac{2005}{20}.$$
Simplify the fraction by dividing by 5 (or by noticing that dividing numerator and denominator by their common factor):
$$\frac{2005}{20} = \frac{401}{4}.$$
Now, convert the improper fraction $\frac{401}{4}$ into a mixed number. Divide 401 by 4:
- The quotient is 100 since $4 \times 100 = 400$.
- The remainder is 1, giving the fraction $\frac{1}{4}$.
Thus, the final answer is
$$100 \frac{1}{4} \text{ pounds}.$$
The construction worker bought $100 \frac{1}{4}$ pounds of nails in the second week.
