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 3/4 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?​

Answer 1

$\huge\tt\fbox{✯Answer✯}$

$\sf{Let\:the\:total\:size\:of\:the\:whale\:be\:x}$

$\sf{Then,\:the\:size\:of\:the\:whales\:body\:is\: \frac{3}{4}x}$

$\sf{And,\:the\:size\:of\:the\:whale's\:tail\:is\:4 + ( \frac{1}{4} \times \frac{3}{4}x} \\ = 4 + \frac{3}{16}$

According to the problem :

$\sf{x - ( \frac{3}{4} + (4 + \frac{3}{16}x)) = 4}$

$\sf{⇒x - ( \frac{3}{4}x + 4 + \frac{3}{16}x) = 4}$

$\sf{⇒x - \frac{3}{4}x + - 4 - \frac{3}{16}x = 4}$

$\sf{⇒x - \frac{3}{4}x - \frac{3}{16}x = 4 \times 4}$

$\sf{⇒ \frac{16x - 12x - 3x}{16} = 8}$

$\sf{⇒ \frac{x}{16} = 8}$

$\sf{⇒x = 8 \times 16}$

$\sf{⇒x = 128}$

Answer↷

Therefore, the total size of the whale is 128 inches .

Answer 2

Step-by-step explanation:

$\huge\sf\overbrace{Given:}$

=>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.

$\huge\sf\overbrace{To \: Find: }$

=> The total length of the whale.

$\huge\sf\overbrace{Solution:}$

=> 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.