High School

One week, a construction worker bought [tex]40 \frac{1}{10}[/tex] pounds of nails. The next week, he bought [tex]2 \frac{1}{2}[/tex] times as many nails as the week before. How many pounds of nails did he buy the second week?

A. [tex]16 \frac{1}{25}[/tex] lb
B. [tex]99 \frac{1}{4}[/tex] lb
C. [tex]80 \frac{1}{20}[/tex] lb
D. [tex]100 \frac{1}{4}[/tex] lb

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.