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

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Write a system of two equations in two unknowns for each problem. Solve each system by substitution. The width of a rectangualr painting is two -thirds of its length. If the per      Log On


   

Question 178257: Write a system of two equations in two unknowns for each problem. Solve each system by substitution.
The width of a rectangualr painting is two -thirds of its length. If the perimeter is 28ft, then what are the length and width?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The width of a rectangular painting is two-thirds of its length. If the perimeter is 28ft, then what are the length and width?
:
Write an equation for each statement;
:
"The width of a rectangular painting is two-thirds of its length.
W = 2%2F3L
:
" If the perimeter is 28ft,"
2L + 2W = 28
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then what are the length and width?
:
Substitute 2%2F3L for W in the perimeter equation, Find L:
2L + 2(2%2F3L) = 28
2L + 4%2F3L = 28
multiply eq by 3 to get rid of that annoying denominator, results:
6L + 4L = 3(28)
:
10L = 84
L= 84%2F10
L = 8.4 ft
:
Find W
2%2F3(8.4) = 5.6 ft
:
:
Check solution:
2(8.4) + 2(5.6) =
16.8 + 11.2 = 28 ft