SOLUTION: helping my 7th grade son with his homework.
What is the method for solving this word problem?
A fish has a four-inch long head. Its tail is as long as its head, plus 1/4 the leng
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What is the method for solving this word problem?
A fish has a four-inch long head. Its tail is as long as its head, plus 1/4 the leng
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Question 233181: helping my 7th grade son with his homework.
What is the method for solving this word problem?
A fish has a four-inch long head. Its tail is as long as its head, plus 1/4 the length of its body. Its body makes up 3/4 of its total length. What is the length of the fish.
I think the answer is 128 but it was solved with trail and error, need help breeaking down the word problem into an equation.
Thanks.. Found 2 solutions by edjones, Theo:Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! Let h=head length, b=body length and t=tail length
h=4
t=4+.25b
b=.75(h+b+t)
b=.75(4+b+4+.25b)
b=.75(1.25b+8)
b=.9375b+6
.0625b=6
b=96
h=4
t=4+ 96/4=4+24=28
96+4+28=128" Total length of the fish.
.
Ed
You can put this solution on YOUR website! A fish has a four-inch long head. Its tail is as long as its head, plus 1/4 the length of its body. Its body makes up 3/4 of its total length. What is the length of the fish.
Let H represent the length of the head.
Let T represent the length of the tail.
Let B represent the length of the body.
Let F represent the length of the fish.
H = 4
T = H + (1/4) * B
B = (3/4) * F
F = H + B + T
First thing to do is replace H with 4 in the equation for T.
You get T = 4 + (1/4) * B
Next thing to do is replace H and T in the equation for B.
B = (3/4) * F
Since F = (H + B + T), this means that:
B = (3/4) * (H + T + B)
Since H = 4, this means that:
B = (3/4) * (4 + T + B)
Since T = (4 + (1/4)*B), this means that:
B = (3/4) * (4 + (4 + (1/4)*B) + B).
Next thing to do is solve for B.
Simplify the expression by completing the indicated operations and removing parentheses starting with the innermost parentheses and working out.
B = (3/4) * (4 + (4 + (1/4)*B) + B) becomes:
B = (3/4) * (4 + 4 + (1/4)*B + B) becomes:
B = (3/4) * (8 + (1/4)*B + (4/4)*B) becomes:
B = (3/4) * (8 + ((5/4) * B)) becomes:
B = ((3/4)*8) + ((3/4) * (5/4) * B) becomes:
B = (24/4) + ((15/16) * B).
Subtract (15/16)*B from both sides to get:
B - (15/16)*B = (24/4)
Factor out the B to get:
B * (1-(15/16) = (24/4)
Simplify to get:
B * (1/16) = (24/4)
Multiply both sides of the equation by (16/1)) to get:
B = (24/4) * (16/1) = (24*16)/(4*1) = (24*4) = 96
T = H + (1/4)*B = 4 + 24 = 28
F = H + T + B = 4 + 28 + 96 = 128.
The body = 96 inches in length.
The head = 4 inches in length.
The tail = 28 inches in length
The fish = 128 inches in length.
The Tail is equal to the head plus 1/4 of the body which equals 4 + 96/4 which e43quals 4 + 24 which equals 28 so this part of the original problem statement is correct.
The Body equals 3/4 of the fish = 3/4 * 128 = 96 so this part of the original problem statement is correct.
Looks like you got it right.
Your answer to the question is that the fish is 128 inches in length.
