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Papessa [141]
3 years ago
12

Use the three steps to solve the problem. the length of a rectangle is 2 inches less than 3 times the number of inches in its wi

dth. if the perimeter of the rectangle is 28 inches, what is the width and length of the rectangle?
Mathematics
1 answer:
Tems11 [23]3 years ago
3 0
Let the width of the rectangle be w.

Let the length be l.

l = 3w - 2

Given,

Perimeter = 28 

2*( l + w ) = 28

2*( 3w -2 + w ) = 28 

4w - 2 = 14  [ Dividing both sides by 2 ]

2w - 1 = 7 [ Dividing both sides by 2 ]

2w = 8

w = 4.

Thus,

l = 3w -2 = 3*4 - 2 = 12 - 2 = 10

Therefore, the length is 10 inches and the width is 4 inches.
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A furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requir
miskamm [114]

The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:

  • 16 chairs; 24 tables
  • Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552
  • Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608  
  • 15 chairs; 18 tables
  • Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450
  • Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480  
  • 12 chairs; 28 tables
  • Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564
  • Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636  
  • 18 chairs; 20 tables
  • Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516
  • Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544

Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:

  • 15 x 65 + 18 x 90 = X
  • 975 + 1,620 = X
  • 2,595 = X

Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Learn more in brainly.com/question/14728529

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