Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables.
-The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters?
Let's define the variables:
Let L be the length of the rectangle.
Let W be the width of the rectangle.
The problem states that "The length of a rectangle is equal to triple the width," so we can write the equation: L = 3W.
The problem also states that "the perimeter is 86 centimeters," so we can write the equation for the perimeter: 2L + 2W = 86.
Now we have a system of equations:
L = 3W
2L + 2W = 86
To solve for all variables, we can use substitution or elimination.
Using substitution:
Substitute L in the second equation with 3W:
2(3W) + 2W = 86
6W + 2W = 86
8W = 86
W = 10.75
Substitute W in the first equation:
L = 3(10.75)
L = 32.25
The dimensions of the rectangle are:
Length = L = 32.25 centimeters
Width = W = 10.75 centimeters