#### Answer

a.) 12 pins
b.) 11$\frac{29}{41}$ or 11 pins

#### Work Step by Step

Total length of the rod = 2 ft 6 in = 2 x 12 + 6 = 30 in.
Number of pins we get after cutting into equal pieces of 2$\frac{1}{2}$ in = 30 in $\div \frac{5}{2}$
= 30 $\times \frac{2}{5}$ = 12 pins
b.) lets take $\frac{1}{16}$ in waste in each pin
so total pin length = 2$\frac{1}{2}$ in + $\frac{1}{16}$ = $ \frac{5}{2} + \frac{1}{16}$ = $ \frac{41}{16}$
therefore total number of pins = 30 $\times \frac{16}{41}$ = $\frac{480}{41}$
=11$\frac{29}{41}$ or 11 pins