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15 strips, 1 1/4" wide are to be ripped from a sheet of plywood. If 1/8" is lost with each cut, how much of the plywood sheet is used to make the 15 strips

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godofconfusion
9/2”

15 strips means 14 cuts so that’s 14/8” lost
14/8 + 11/4 (or 22/8) = 36/8 = 9/2”

The plywood needed for 15 strips is 20.5 inches.

Given to us

  • Number of strips needed = 15
  • width of the strip = [tex]\rm 1\dfrac{1}{4}\ inches[/tex]
  • Lost of the plywood to cut a strip =  [tex]\rm{ \dfrac{1}{8}\ inches[/tex]

width of the strip

[tex]\rm 1\dfrac{1}{4}\ inches = \dfrac{(4 \times 1) +1 }{4} =\dfrac{5}{4}\ inches[/tex]

Number of cuts

As to cut 15 strips of plywood a total of 14 cuts will be needed.

therefore, the waste of plywood in these 14 strips will be

= Lost in each cut x Number of cuts

[tex]=\dfrac{1}{8}\times 14\\\\=\dfrac{14}{8}\\\\ = \dfrac{7}{4} inches[/tex]

Total plywood needed for all strips

Total plywood needed for all single strip

                        = width of the strip x number of strips

                        [tex]=\dfrac{5}{4} \times 15\\\\ =\dfrac{75}{4}\\\\[/tex]

Plywood needed

Plywood needed

= Total plywood needed for all strip +  Total waste of plywood

[tex]=\dfrac{7}{4}+\dfrac{75}{4}\\\\=\dfrac{82}{4}\\\\=20.5\ \rm inches[/tex]

Hence, the plywood needed for 15 strips is 20.5 inches.

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