SOLUTION: A fish was caught whose tail weighed 9 lb. Its head weighed as much as it's tail pluse half its body. Its body weighed as much as it's head and tail. What did the fish weigh?

Algebra ->  Test -> SOLUTION: A fish was caught whose tail weighed 9 lb. Its head weighed as much as it's tail pluse half its body. Its body weighed as much as it's head and tail. What did the fish weigh?      Log On


   



Question 368101: A fish was caught whose tail weighed 9 lb. Its head weighed as much as it's tail pluse half its body. Its body weighed as much as it's head and tail. What did the fish weigh?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = weight of tail
Let b = weight of body
Let h = weight of head
given:
t+=+9
h+=+t+%2B+b%2F2
b+=+h+%2B+t
---------------
By substitution:
h+=+9+%2B+b%2F2
2h+=+18+%2B+b
(1) 2h+-+b+=+18
and
b+=+h+%2B+9
(2) h+-+b+=+-9
Subtract (2) from (1)
(1) 2h+-+b+=+18
(2) -h+%2B+b+=+9
h+=+27
And, since,
b+=+h+%2B+9
b+=+27+%2B+9
b+=+36
The fish weighed 9+%2B+27+%2B+36+=+72 pounds
check answer:
h+=+t+%2B+b%2F2
27+=+9+%2B+36%2F2
27+=+9+%2B+18
27+=+27
and
b+=+h+%2B+t
36+=+27+%2B+9
36+=+36
OK