A boy purchased a sandwich 52 inches long he wants to cut into three pieces so that the middle piece is 5 inches longer than the shortest piece and the shortest piece is 8 inches shorter than the longest piece how long should all three pieces be

The pieces are

x, y, z

longest to shortest

y is 5 more than z

y=5+z

z is 8 less than x

z=x-8

find everything in terms of x

y=5+z

sub z=x-8

y=5+x-8

y=x-3

so we got

x=x

y=x-3

z=x-8

total length is 52

x+y+z=52

x+x-3+x-8=52

x+x+x-3-8=52

3x-11=52

add 11 to both sides

3x+11-11=52+11

3x=63

divide both sides by 3

x=21

y=x-3=21-3=18

z=x-8=21-8=13

the pieces are 13in, 18in, 21in