A rare whale fossil was uncovered under layers of sediment. When the excavator took measurements, she found the tail to be as long

Question

A rare whale fossil was uncovered under layers of sediment. When the excavator took measurements, she found the tail to be as long as its head plus a quarter of the length of the body. When the archaeologist came in, he measured the length of the body. He found it to be ¾ of the total length. They made arguments about how such a fish would swim in the water. To make proper predictions they measured the head size, and found it to be 4 inches long. What is the total length of this whale?
A)128 B)99 C)136 D)142
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Melanie · Answer

Step-by-step explanation:     huge bf underline{Given:}   => The tail is to be as long as it's head plus a quarter of the length of the body.  => Length of body be ¾ of the length.  => Head is 4 inches long.    huge bf underline{To   : Find:}   => The total length of whale.    huge bf underline{Solution:}   => Head = 4 inch  => Body = x inch  => Tail = Head + 1/4x  => Tail = 4 + x/4 inches.    Total length = Head + Body + Tail  => 4+x+4+x/4  => 8 + 5x/4    Body = 3/4T Total length  x = 3/4 (8 + 5x/4)  4x = 3 × 32 + 5x/4  16x = 96 + 15x  x = 96    Total length = 8 + 5 × 96/4  => 8 + 5 × 24  => 8 + 120  => 128    huge sf overbrace{Answer}   => Head = 4 inches  => Body = 96 inches  => Tail = 28 inches  Therefore, The total length of the whale is 128inches.

Ariana · Answer

Large underbrace pink{Answer}    1  2  8     i  n  c  h  e  s           large underbrace green{solution :steps}       sf{➟Let :the :total :size :of :the :whale's :body :be :x}         sf{Then, :the :size :of :the :whale's :body :is  frac{3}{4} x}       sf{And, :the  : size  : of  : the  : whale  : tail  : is  : 4 + (  frac{1}{4}   times   frac{3}{4}) x}       bf red{According :to :the :question:}       sf{x - (  frac{3}{4}  + (4 +   frac{3}{16} x)) = 4}       sf{⇒x - (  frac{3}{4} x + 4 +   frac{3}{16} x) = 4}       sf{⇒x -   frac{3}{4} x  - 4 -   frac{3}{16} x = 4}       sf{⇒x -   frac{3}{4} x -   frac{3}{16} x = 4 + 4}       sf{⇒  frac{16x - 12x - 3x}{16}  = 8}       sf{⇒  frac{x}{16}  = 8}       sf{⇒x = 8  times 16}       sf{⇒x = 128}         bf purple{Answer:}    The total size of the whale is  1  2  8    inches.

Luna

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