SOLUTION: a to b is 5 km more than d to e, c to d is twice the distance from a to b, c is midway between b and d. if the total from a to e is 91 km find the distance from d to e

Question 717557: a to b is 5 km more than d to e, c to d is twice the distance from a to b, c is midway between b and d. if the total from a to e is 91 km find the distance from d to e
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a to b is 5 km more than d to e, c to d is twice the distance from a to b, c is midway between b and d. if the total from a to e is 91 km find the distance from d to e
:
let w = ab distance
let x = bc
let y = cd
let z = de
:
a-----w------b------x-------c-------y------d-------z-------e
:
"a to b is 5 km more than d to e,"
w = z+5
z = w-5
:
" c to d is twice the distance from a to b,"
y = 2w
:
"c is midway between b and d." (bc = cd)
x = y
:
"the total from a to e is 91 km"
w + x + y + z = 91
If y = 2w, then x = 2w, also we know z = w-5
w + 2w + 2w + (w-5) = 91
combine like terms
6w = 91 + 5
6w = 96
w = 96/6
w = 16
:
"find the distance from d to e, (that's z)
z = 16 - 5
z = 11 is the distance from d to e
;
:
:
See if that checks out
16 + 2(16) + 2(16) + 11 = 91
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