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Answer :
To determine how many pounds of nails the construction worker bought the second week, we need to follow these steps:
1. Identify the amount of nails bought the first week:
The construction worker bought [tex]\( 40 \frac{1}{10} \)[/tex] pounds of nails in the first week. This can be written as a mixed number:
[tex]\[
40 \frac{1}{10} = 40 + \frac{1}{10}
\][/tex]
2. Determine the quantity for the second week:
The next week, he bought [tex]\( 2 \frac{1}{2} \)[/tex] times as many nails as the week before. In fractional form, this is:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2}
\][/tex]
3. Calculate the total for the second week:
To find out how many pounds of nails were bought the second week, multiply the amount from the first week by the multiplier:
[tex]\[
\left(40 + \frac{1}{10}\right) \times \left(2 + \frac{1}{2}\right)
\][/tex]
4. Result:
By performing the multiplication, we find that the construction worker bought 100.25 pounds of nails the second week. This can be expressed as:
[tex]\[
100 \frac{1}{4}
\][/tex]
5. Choose the correct answer:
From the given options, the closest match to [tex]\( 100 \frac{1}{4} \)[/tex] pounds is option D.
Thus, the correct answer is [tex]\( \boxed{100 \frac{1}{4} \text{ lb}} \)[/tex].
1. Identify the amount of nails bought the first week:
The construction worker bought [tex]\( 40 \frac{1}{10} \)[/tex] pounds of nails in the first week. This can be written as a mixed number:
[tex]\[
40 \frac{1}{10} = 40 + \frac{1}{10}
\][/tex]
2. Determine the quantity for the second week:
The next week, he bought [tex]\( 2 \frac{1}{2} \)[/tex] times as many nails as the week before. In fractional form, this is:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2}
\][/tex]
3. Calculate the total for the second week:
To find out how many pounds of nails were bought the second week, multiply the amount from the first week by the multiplier:
[tex]\[
\left(40 + \frac{1}{10}\right) \times \left(2 + \frac{1}{2}\right)
\][/tex]
4. Result:
By performing the multiplication, we find that the construction worker bought 100.25 pounds of nails the second week. This can be expressed as:
[tex]\[
100 \frac{1}{4}
\][/tex]
5. Choose the correct answer:
From the given options, the closest match to [tex]\( 100 \frac{1}{4} \)[/tex] pounds is option D.
Thus, the correct answer is [tex]\( \boxed{100 \frac{1}{4} \text{ lb}} \)[/tex].
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