Question 1162695
let the length of each piece be a, b, c, d.
you get:
a + b + c + d = 96
you get the following additional equations based on the problem statement.
b = 2a - 6
c = a + 5
d = b/2
the trick is to reduce the number of variables to 1.
then the problem can be solved.
we'll try to make everything in terms of a.
d = b/2 is not in terms of a, but we know that b = 2a - 6
replace b in the equation of d = b/2 to get d = (2a - 6) / 2
now you have everything in terms of a.
you have:
b = 2a - 6
c = a + 5
d = (2a - 6) / 2
a + b + c + d = 96 becomes:
a + (2a - 6) + (a + 5) + (2a - 6) / 2 = 96
simplify to get:
a + 2a - 6 + a + 5 + 2a/2 - 6/2 = 96
simplify further to get:
a + 2a - 6 + a + 5 + a - 3 = 96
combine like terms to get:
5a - 4 = 96
add 4 to both sides of the equation to get:
5a = 100
solve for a to get:
a = 100 / 5 = 20
b = 2a - 6 = 40 - 6 = 34
c = a + 5 = 25
d = b / 2 = 17
a + b + c + d = 20 + 34 + 25 + 17 = 96
solution is confirmed to be good.
solution is the fourth piece (piece d) is 17 feet in length.