SOLUTION: Write a system of two equations in two unknowns. Solve each system by substitution. The width of a rectangualr painting is two- thirds of its length. If the perimeter is 60in.,

Question 178378: Write a system of two equations in two unknowns. Solve each system by substitution.
The width of a rectangualr painting is two- thirds of its length. If the perimeter is 60in., then what are the length and width?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The width of a rectangualr painting is two- thirds of its length. If the perimeter is 60in., then what are the length and width?
.
Let W = width
and L = length
then
from: "The width of a rectangualr painting is two- thirds of its length."
W = (2/3)L (equation 1)
.
from: "the perimeter is 60in"
2(W+L) = 60 (equation 2)
.
Substitute the definition of W from equation 1 into equation 2 and solve for L:
2(W+L) = 60
2((2/3)L+L) = 60
2((2/3)L+(3/3)L) = 60
2((5/3)L) = 60
(5/3)L = 30
5L = 90
L = 18 inches (length)
.
Plug the above into equation 1 and solve for W:
W = (2/3)L
W = (2/3)18
W = (2)6
W = 12 inches (width)
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