---------------------------------------------------------------- Define x and y: ---------------------------------------------------------------- Let the length be x. Let the width be y.
---------------------------------------------------------------- Construct equations and solve for x and y: ---------------------------------------------------------------- 2x + 2y = 56 ---------------------- (1) 2(x+8) + 4y = 82 -----------------------(2)
---------------------------------------------------------------- From equation 1: ---------------------------------------------------------------- 2x + 2y = 56 x + y = 28 x = 28 - y
---------------------------------------------------------------- Substitute x = 28 - y into equation 2: ---------------------------------------------------------------- x + 2y = 33 (28 - y) + 2y = 33 28 - y + 2y = 33 y = 5
---------------------------------------------------------------- Substitute y = 5 into equation 1: ---------------------------------------------------------------- x = 28 - y x = 28 - 5 x = 23
---------------------------------------------------------------- Find Length and Width ---------------------------------------------------------------- Length = x = 23 m Width = y = 5m
---------------------------------------------------------------- Answer: Length = 23m and Width = 5m ----------------------------------------------------------------
If you're not familiar with the multinomial coefficient, you may be able to see it more clearly if you count the number of possible combinations taking each distinct letter times, where is the number of times it shows up in the original word.
times, where 