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?​

Answer 1

$\Large\tt\fbox\pink{Answer}$

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

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

$\sf{And \: the \: size \: of \: the \: whale \: tail \: is \: 4 + ( \frac{1}{4} \times \frac{3}{4})x}$

$\sf\red{According\:to\:the \: problem:}$

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

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

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

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

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

$\sf{⇒ \frac{x}{16} = 8}$

$\sf{⇒x = 8 \times 16}$

$\sf{⇒x = 128}$

$\small\bf\fbox{Answer}$

The total size of the whale is 128 inches.

Answer 2

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.