Question

Please help me with this Algebra problem: The length of a rectangle is 91 less than six times the width of the rectangle. If the perimeter of the rectangle is 84 centimeters, what is the length of the rectangle? Write a system of equations for this situation and find its solution.
I have so far: P = 2L + 2W P = 2 (6x-91) + 2W P = 12x -182 + 2W 2 (6x-91) =84 12x -182 =84 12x =266 Please help...I am confused...thank you

Answer 1

 182 Let x = width then y = 6x - 91. P (perimeter) = 2x + 2y = 84 then

2(x) + 2(6x - 91) = 84 | 2x + 12x - 182 =84 | 14x = 84 + 182 | 14x = 266 | x = 19 cm

y = 6x - 91 | y = 6 (19) - 91 | y = 114 - 91 | y = 23 cm

Check: P = 2x + 2y | P = 2(19) + 2(23) | P = 38 + 46 | P = 84 cm (Checked)