A Steel Rod $36$ Inches Long Has Twelve Pieces Cut to the Following Lengths

A steel rod $36$ inches long has twelve pieces cut to the following lengths: 3 pieces, $2 \frac { 1 } { 8 }$ inches in length
2 pieces, $5 \frac { 3 } { 4 }$ inches in length
6 pieces, $\frac { 7 } { 8 }$ inches in length
1 piece, $3 \frac { 1 } { 2 }$ inches in length
Assume $\frac { 1 } { 16 }$ of an inch is wasted with each cut. Find the length of the remaining rod.

A) $8 \frac { 5 } { 8 }$ inches
B) $5 \frac { 5 } { 8 }$ inches
C) $13 \frac { 5 } { 8 }$ inches
D) $7 \frac { 5 } { 8 }$ inches
E) $10 \frac { 5 } { 8 }$ inches

Correct Answer:

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