Question 338568
Write an equation for each statement:
:
Two times the length plus two times the width equals the perimeter of a rectangle.
2L + 2W = P
:
 The perimeter of the rectangle is 56 meters.
2L + 2W = 56
:
Twice the length of the rectangle is one more than three times the width.
2L = 3W + 1
:
Looking at this we can replace 2L in the 2nd equation with (3W+1), so we have:
(3W+1) + 2W = 56
5W + 1 = 56
5W = 56 - 1
5W = 55
W = {{{55/5}}}
W = 11 m is the width
then
we know 2L = 3W + 1; replace W with 11
2L = 3(11) + 1
2L = 33 + 1
L = {{{34/2}}}
L = 17 m is the length
:
;
Check this in the perimeter equation
2(17) + 2(11) = 56
34 + 22 = 56
and 
2L = 3W + 1
34 = 3(11) + 1; confirms our solution: L = 17; W = 11