A CAD drawing shows a bar 2 inches thick, by 4 inches wide, by 30 inches in length, ready to be cut into smaller pieces. Each saw cut wastes $\frac { 1 } { 3 }$ of an inch of the bar. How many $3 \frac { 1 } { 3 }$ inch pieces can be cut?
A) $8$ pieces
B) $6$ pieces
C) $9$ pieces
D) $14$ pieces
E) $7$ pieces

Question

A CAD drawing shows a bar 2 inches thick, by 4 inches wide, by 30 inches in length, ready to be cut into smaller pieces. Each saw cut wastes $\frac { 1 } { 3 }$ of an inch of the bar. How many $3 \frac { 1 } { 3 }$ inch pieces can be cut? 
A) $8$ pieces 
B) $6$ pieces 
C) $9$ pieces 
D) $14$ pieces 
E) $7$ pieces

Quizplus · Accepted Answer

If we subtract the wasted portion of each cut from the length of the bar, we get the effective length of each piece:

\begin{align*}
30 - \frac{1}{3} &= 29 \frac{2}{3} \text{ inches}\
29 \frac{2}{3} - \frac{1}{3} &= 29 \frac{1}{3} \text{ inches}\
29 \frac{1}{3} - \frac{1}{3} &= 29 \text{ inches}\
29 - \frac{1}{3} &= 28 \frac{2}{3} \text{ inches}\
28 \frac{2}{3} - \frac{1}{3} &= 28 \frac{1}{3} \text{ inches}\
28 \frac{1}{3} - \frac{1}{3} &= 28 \text{ inches}\
28 - \frac{1}{3} &= 27 \frac{2}{3} \text{ inches}\
27 \frac{2}{3} - \frac{1}{3} &= 27 \frac{1}{3} \text{ inches}\
27 \frac{1}{3} - \frac{1}{3} &= 27 \text{ inches}
\end{align*}

We can see that each effective length is a multiple of $3 \frac{1}{3}$ inches. Therefore, we can cut a total of:

\begin{align*}
\frac{30}{3 \frac{1}{3}} &= 9 \text{ pieces}
\end{align*}

So the answer is \boxed{\textbf{(C)}}.

A CAD Drawing Shows a Bar 2 Inches Thick, by 4