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Two splice plates are cut from a piece of sheet steel that has an overall length of 17 1/2 in. The plates are 9 3/8 in. and 6 15/16 in. long. How much material remains from the original piece if each saw cut removes 1/16 ​in.? ____ in. of material remains from the original piece. ​(Type a whole​ number, proper​ fraction, or mixed​ number.)

Respuesta :

Answer: [tex]\frac{3}{4}\ in[/tex] of material remains from the original piece.

Step-by-step explanation:

Since we have given that

Overall length of steel sheet is given by

[tex]17\frac{1}{2}\ in=\frac{35}{2}\ in[/tex]

Size of first plate is given by

[tex]9\frac{3}{8}\ in=\frac{75}{8}\ in[/tex]

Size of second plate is given by

[tex]6\frac{15}{16}\ in\\\\=\frac{111}{16}\ in[/tex]

Wastage of material from first plate is given by

[tex]\frac{1}{16}\ in[/tex]

Wastage of material from second plate is given by

[tex]\frac{1}{16}\ in[/tex]

According to question, Amount remains from the original piece is given by

[tex]\frac{35}{2}-(\frac{75}{8}+\frac{111}{16}+\frac{1}{16}+\frac{1}{16})\\\\\frac{35}{2}-\frac{150+116+1+1}{16}\\\\=\frac{35}{2}-\frac{268}{16}\\\\=\frac{280-268}{16}\\\\=\frac{12}{16}\ in\\\\=\frac{3}{4}\ in[/tex]

Hence, [tex]\frac{3}{4}\ in[/tex] of material remains from the original piece.

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