Megalodon Lives

Angler went fishing and caught a monster of a fish! The head of the fish was 10 feet long. The length of the tail was equal to the length of the head plus half of the body. The body was as long as the head and the tail together. What was the total length of the Megalodon? ______
Set up as a system of equations and use the substitution method to solve your problem...Show work!!!

Head = 10 Ft long,

Body = X Ft long.
Tail = (X/2 + 10) Ft long.

T + H = B.
(X/2 + 10) + 10 = X
X/2 + 20 = X,
X + 40 = 2x,
2x - X = 40,

B = X = 40 Ft. = Length of body.
T = X/2 + 10 = 40/2 + 10 = 30 Ft.
H = 10 Ft.

To set up a system of equations, let's denote the length of the head as h, the length of the tail as t, and the length of the body as b.

According to the problem, we have the following information:

1. The head of the fish was 10 feet long: h = 10.
2. The length of the tail was equal to the length of the head plus half of the body: t = h + (1/2)b.
3. The body was as long as the head and the tail together: b = h + t.

We can substitute the values of h and b in the second and third equations using the first equation to create a system of equations.

Substitute h = 10 into the second equation:
t = 10 + (1/2)b.

Substitute h = 10 and b = h + t into the third equation:
b = 10 + t.

Now we have a system of equations:
t = 10 + (1/2)b,
b = 10 + t.

To solve the system using substitution method, we can substitute b = 10 + t into the first equation:
t = 10 + (1/2)(10 + t).

Now let's solve for t:
t = 10 + (5 + 1/2t).
t = 15 + 1/2t.
t - 1/2t = 15.
1/2t = 15.
t = 30.

Now we have the value of t, which is the length of the tail. To find the length of the body, substitute t = 30 into the third equation:
b = 10 + 30.
b = 40.

Finally, to find the total length of the Megalodon, we add up the head, tail, and body lengths:
Total length = h + t + b = 10 + 30 + 40 = 80 feet.

Therefore, the total length of the Megalodon is 80 feet.