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
P = 2L + 2W
84 = 2 (6W-91) + 2W
84 = 14W - 182
266 = 14W
19 = Width
Why do you have L's, W's and x's in your equation ?
width ---- w
length ---- l
equation #1:
2w + 2l = 84
w+l = 42 **
equation #2:
"The length of a rectangle is 91 less than six times the width of the rectangle"
---> l = 6w - 91
sub that back into **
w + 6w-91 = 42
7w = 133
w = 133/7 = 19
back in
l = 6w-91
= 6(19)-91 = 23
To solve this problem, you need to set up a system of equations based on the given information.
Let's consider the length of the rectangle as L and the width as W.
From the information given, we know that the length of the rectangle is 91 less than six times the width, which can be written as:
L = 6W - 91
The perimeter (P) of a rectangle is the sum of the lengths of all its sides. In this case, we have two lengths (L) and two widths (W). Therefore, the perimeter can be written as:
P = 2L + 2W
Now, substitute the value of L from the first equation into the second equation:
P = 2(6W - 91) + 2W
Simplifying, we get:
P = 12W - 182 + 2W
P = 14W - 182
The perimeter is given as 84 centimeters, so we can now rewrite the equation as:
84 = 14W - 182
Adding 182 to both sides, we have:
14W = 266
Now, divide both sides of the equation by 14 to solve for W:
W = 266/14
W = 19
So, the width of the rectangle is 19 centimeters.
To find the length, substitute the value of W into the first equation:
L = 6W - 91
L = 6(19) - 91
L = 114 - 91
L = 23
Therefore, the length of the rectangle is 23 centimeters.
So, the solution to the system of equations is width (W) = 19 cm and length (L) = 23 cm.