A 3 foot long 36 inches deli sandwich must be split into thr

A 3 foot long (36 inches) deli sandwich must be split into three pieces so that the middle piece is twice as long as the shortest piece and the shortest piece is 8 inches shorter than the longest. How long should the three pieces be?

Solution

the length of the 3 foot long deli sandwich is = 36 inches;
Let the length of its 3 portions be x,y,z, (in inches) such that x>y>z (in length)
we know that x+y+z = 36;
y = 2z (since middle piece is twice as long as shortest piece)
x= z+8 (since the shortest piece is 8 inches shorter than the longest)
substituting these values in x+y+z = 36 we get:

z+8 + 2z + z = 36
4z+8 = 36 so 4z = 28 and z= 28/4 = 7;
if z=7, y = 2*7 = 14;
x = 7+8 = 15;
Hence the sandwich is cut into 3p ieces of length 7,14,15;