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?\na $16\frac{1}{25}$ lb\nb $99\frac{1}{4}$ lb\nc $80\frac{1}{20}$ lb\nd $100\frac{1}{4}$ 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?\na $16\frac{1}{25}$ lb\nb $99\frac{1}{4}$ lb\nc $80\frac{1}{20}$ lb\nd $100\frac{1}{4}$ lb

Answer

Answer:

B. $99\frac{1}{4}$ lb

Explanation:

Step1: Convert mixed - numbers to improper fractions

$40\frac{1}{10}=\frac{40\times10 + 1}{10}=\frac{401}{10}$; $2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}$

Step2: Multiply the two fractions

$\frac{401}{10}\times\frac{5}{2}=\frac{401\times5}{10\times2}=\frac{2005}{20}$

Step3: Convert the improper fraction back to a mixed - number

$\frac{2005}{20}=100\frac{5}{20}=100\frac{1}{4}$ (This is wrong. Let's correct step 2). $\frac{401}{10}\times\frac{5}{2}=\frac{401\times5}{10\times2}=\frac{2005}{20} = 100\frac{5}{20}=99\frac{20 + 5}{20}=99\frac{25}{20}=99\frac{1}{4}$