Question

a construction worker bought $21\frac{1}{4}$ pounds of nails. when those nails were all used, he bought $1\frac{1}{2}$ times as many nails as he had bought the first time. how many pounds of nails did he buy the second time?
a $31\frac{7}{8}$ lb
b $21\frac{1}{8}$ lb
c $30\frac{7}{8}$ lb
d $14\frac{1}{6}$ lb

Explanation:

Step1: Convert mixed numbers to improper fractions

First purchase: $21\frac{1}{4} = \frac{21\times4 + 1}{4} = \frac{85}{4}$
Multiplier: $1\frac{1}{2} = \frac{1\times2 + 1}{2} = \frac{3}{2}$

Step2: Multiply to find second purchase

Multiply the two fractions: $\frac{85}{4} \times \frac{3}{2} = \frac{85\times3}{4\times2} = \frac{255}{8}$

Step3: Convert back to mixed number

$\frac{255}{8} = 31\frac{7}{8}$

Answer:

A. $31\frac{7}{8}$ lb