How long is the fish ? homework help

Question

jim caught a fish its head is 5" long. the tail is as long as the head plus half the body. the body is al long as the head plus the tail. how long is the fish ?

Answer 1

20" or 25"

Answer 2

Let x = the length of the body of the fish in inches.

The head of the fish is 5 inches long.

The tail of the fish is as long as the head (5 inches) + 1/2 of the length of the body of the fish.  Therefore, the tail is 1/2(x) +5 inches.

The body of the fish is as long as the head + the tail.  Therefore, the body of the fish is equal to 5 inches (head size) + (1/2(x) + 5 inches) ( tail size)

Therefore the body of the fish (x) is equal to 1/2(x) + 5 inches + 5 inches OR x = 1/2(x) +10 inches OR

1/2(x) = 10 inches

x = 20 inches = the length of the body of the fish.

The tail is equal to 1/2(x) where x = 20 inches OR 10 inches + the length of the head which is 5 inches for a total tail length of 15 inches.

Therefore, the length of the fish is equal to the length of the head (5 inches) plus the length of the body (20 inches) plus the length of the tail (15 inches) for a total fish length of 40 inches.

  

Answer 3

This problem is solved with a bit of algebra and insight.

The fish's length is split into 3 parts: head, body and tail. We know that the head (H) is 5 inches long (H=5), the tail (T) is the length of H plus half the body so T = H+1/2B, and the body is H+T.

The key to the solution is to solve for the length of the body.

Body = H+T

         = H+(H+1/2B)

         = 2H + 1/2/B

2H we know is 10 inches, so Body = 10 + 1/2B; and, since we know that a whole is made of 2 halves, 1/2B must also equal 10. Therefore, the length of the body is 20 inches. This makes the tail 5+1/2(20) = 15 inches.

The length of the Jim's fish is 40 inches (5+20+15).

Answer 4

Body=Head +tail; Tail=H+(B/2):::B=H+( H+T/2);;;2T=2H+(2H+T):::B=4H ;;;;;;;H=5", B=20", T=15"