Question

A shark was caught whose tail weighed 200 pounds. The head of the shark weighed as much as its tail plus half its body. It’s body weighed as much as its head and tail. What is the weight if the shark?

Answer 1

Answer:1600

Step-by-step explanation:To solve this problem, we’ll have 3 variables

T for weight of tail

H for weight of head

B for weight of body

We know that T = 200 pounds

The head of the shark is the weight of the tail + half the body. Therefore, we can use the formula:

H = T + 0.5B

The body weighs as much as the head and tail. That will be

B = H + T

We can substitute H + T in the place of B in the H equation, so we get

H = T + 0.5H + 0.5T

Combining like terms, we get: 0.5H = 1.5T

Because T = 200 pounds, we can say 0.5H = 1.5 * 200, which simplifies to 0.5H = 300

Divide both sides by 0.5 and get H = 600 pounds

We can then find the weight of the body to be H + T, which is 200 + 600, and that adds up to 800 pounds

The total weight of the body is B + H + T, which equals 200 + 600 + 800, which is 1600 pounds.

Answer 2

Answer: Lets denote:

Tail by T

Head by H

and Body by B

Given info:

Statement 1: Head weighs as much as the tail plus half of it’s body

H =T + 1/2B

Thus,

H = 200 + 1/2 B …. Equation 1

Statement 2: Body weighs as much as head and tail.

B = H + T

B = H + 200 …. Equation 2

substituting value of B from equation 2 into 1.

H = 200 + 1/2H + 100

1/2H = 300

H = 600

B = 800

Shark’s weight = (H+T+ B) = 1600 pounds