the tail weighed 9 pounds. the hyead weighed as much as the tail plus 1/3 of the body combined, and the body weighed as much as the head and tail combined. what was the total weight of the fish?
t=9
h = t + b/3
b = h+t
knowing t=9, we have
h = 9 + b/3
b = h+9
so,
h = 9 + (h+9)/3
h = 9 + h/3 + 3
2h/3 = 12
h = 18
b = 27
t = 9
add 'em up for the total weight
To solve this problem, let's break it down step by step.
Let's assign variables to each part of the fish:
- Let "T" represent the weight of the tail.
- Let "H" represent the weight of the head.
- Let "B" represent the weight of the body.
Based on the given information, we can form the following equations:
1) The head weighs as much as the tail plus 1/3 of the body combined:
H = T + (1/3)B
2) The body weighs as much as the head and tail combined:
B = H + T
Now, we can substitute equation 2 into equation 1:
H = T + (1/3)(H + T)
Next, we simplify equation 1:
H = T + (1/3)H + (1/3)T
To simplify further, we can remove the parentheses:
H = T + (1/3)H + (1/3)T
H = (4/3)T + (1/3)H
Combine like terms by subtracting (1/3)H from both sides:
H - (1/3)H = (4/3)T + (1/3)H - (1/3)H
(2/3)H = (4/3)T
Multiply both sides of the equation by (3/2) to eliminate the fraction:
(2/3)H * (3/2) = (4/3)T * (3/2)
H = (2/1)T
This equation implies that the weight of the head is twice the weight of the tail.
Now, let's use the information given to determine the weight of the fish. Given that the tail weighs 9 pounds, we can calculate the weight of the head:
H = 2T
H = 2 * 9
H = 18 pounds
Since the body weighs as much as the head and tail combined, we can calculate the weight of the body:
B = H + T
B = 18 + 9
B = 27 pounds
Finally, to find the total weight of the fish, we add the weight of the tail, head, and body:
Total weight = T + H + B
Total weight = 9 + 18 + 27
Total weight = 54 pounds
Therefore, the total weight of the fish is 54 pounds.