Question

a 50 meter path surrounds a rectangular garden. the width of the garden is two thirds it's length. find the length and width

Answer 1

W = 2L / 3 and 2W + 2L = 50. Substitute 2L / 3 for W in the second equation to get: 
2(2L/3) + 2L = 50 
4L/3 + 6L/3 = 50 
10L/3 = 50 
L = 3 * 50 / 10 = 15. Replace L for 15 in the first equation: 

W = 2(15) / 3 
W = 10

Answer 2

 W = 2L / 3 and 2W + 2L = 50. Substitute 2L / 3 for W in the second equation to get: 2(2L/3) + 2L = 50. 4L/3 + 6L/3 = 50