SOLUTION: Joshua Rogers has a sheet of tin 12cm by 16cm. He plans to make a box by cutting equal squares out of each of the four corners and folding up the remaining edges. How large a squar

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Joshua Rogers has a sheet of tin 12cm by 16cm. He plans to make a box by cutting equal squares out of each of the four corners and folding up the remaining edges. How large a squar      Log On


   

Question 457211: Joshua Rogers has a sheet of tin 12cm by 16cm. He plans to make a box by cutting equal squares out of each of the four corners and folding up the remaining edges. How large a square should he cut so that the finished box will have a length that is 5 cm less than twice the width?
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Answer by amoresroy(361) About Me  (Show Source):
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Joshua Rogers has a sheet of tin 12cm by 16cm. He plans to make a box by cutting equal squares out of each of the four corners and folding up the remaining edges. How large a square should he cut so that the finished box will have a length that is 5 cm less than twice the width?
Let x = the number of cm the square should be cut
L = the length of the finished box
W = the width of the finished box
Equations:
L = 2W -5
Where:
L = 16-2x
and
W = 12-2x
Eliminating x you get
L = W +4
Substituting L=W+4 in first equation you get
W + 4 = 2W - 5
W = 9
Substituting W=9 in 3rd equation you get
2x = 12 - 9
x = 1.5
The square should he cut by 1.5 cm so that the finished box will have a length that is 5 cm less than twice the width.
Warm regards,
Roy