SOLUTION: 1. A rectangular light-switch plate is made according to the following dimensions. The length is 8 inches, and the width is 6 inches; a rectangular hole measuring 1 inch by 3 inche
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Question 198672: 1. A rectangular light-switch plate is made according to the following dimensions. The length is 8 inches, and the width is 6 inches; a rectangular hole measuring 1 inch by 3 inches is left in the center. (See diagram below) (a) How many square inches in area is the light-switch plate (the shaded region)? (b) If the cost to construct the plate is $3.50 per square inch, what is the construction cost? Found 2 solutions by nerdybill, solver91311:Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! A rectangular light-switch plate is made according to the following dimensions. The length is 8 inches, and the width is 6 inches; a rectangular hole measuring 1 inch by 3 inches is left in the center. (See diagram below) (a) How many square inches in area is the light-switch plate (the shaded region)? (b) If the cost to construct the plate is $3.50 per square inch, what is the construction cost?
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a)
"area of light-switch plate" = "area of plate" - "rectangular hole"
"area of light-switch plate" = (8)(6) - (1)(3)
"area of light-switch plate" = 48 - 3
"area of light-switch plate" = 45 square inches
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b)
cost = 45*3.50 = $157.50
The area of the entire switchplate, including the hole in the center is just the length times the width. The area of the hole is the length times the width of the hole. Subtract the area of the hole from the overall area of the switchplate to get the desired area. Multiply that area by 3.5 to get the construction cost. Mighty expensive switch plate if you ask me.
