one week, a construction worker bought $40\\frac{1}{10}$ pounds of nails. the next week, he bought…

one week, a construction worker bought $40\\frac{1}{10}$ pounds of nails. the next week, he bought $2\\frac{1}{2}$ times as many nails as the week before. how many pounds of nails did he buy the second week? a $16\\frac{1}{25}$ lb b $99\\frac{1}{4}$ lb c $80\\frac{1}{20}$ lb d $100\\frac{1}{4}$ lb

one week, a construction worker bought $40\\frac{1}{10}$ pounds of nails. the next week, he bought $2\\frac{1}{2}$ times as many nails as the week before. how many pounds of nails did he buy the second week? a $16\\frac{1}{25}$ lb b $99\\frac{1}{4}$ lb c $80\\frac{1}{20}$ lb d $100\\frac{1}{4}$ lb

Answer

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert (40\frac{1}{10}) to an improper fraction: (40\frac{1}{10}=\frac{40\times10 + 1}{10}=\frac{401}{10}). Then, convert (2\frac{1}{2}) to an improper fraction: (2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}).

Step2: Multiply the two fractions

Multiply (\frac{401}{10}) by (\frac{5}{2}): (\frac{401}{10}\times\frac{5}{2}=\frac{401\times5}{10\times2}). Simplify (\frac{401\times5}{10\times2}): (\frac{401\times5}{10\times2}=\frac{401}{2\times2}=\frac{401}{4}).

Step3: Convert the improper fraction back to a mixed number

Divide (401) by (4): (401\div4 = 99\frac{5 - 4}{4}=99\frac{1}{4}).

Answer:

B. (99\frac{1}{4}) lb