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?
Step-by-step explanation:
[tex]\huge\sf\overbrace{Given:}[/tex]
=>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.
[tex]\huge\sf\overbrace{To \: Find: }[/tex]
=> The total length of the whale.
[tex]\huge\sf\overbrace{Solution:}[/tex]
=> 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
[tex]\huge\sf\overbrace{Answer}[/tex]
=> Head = 4 inches
=> Body = 96 inches
=> Tail = 28 inches
Therefore, The total length of the whale is 128inches.
[tex]\huge\tt\fbox{✯Answer✯}[/tex]
[tex]\sf{Let\:the\:total\:size\:of\:the\:whale\:be\:x}[/tex]
[tex]\sf{Then,\:the\:size\:of\:the\:whales\:body\:is\: \frac{3}{4}x}[/tex]
[tex]\sf{And,\:the\:size\:of\:the\:whale’s\:tail\:is\:4 + ( \frac{1}{4} \times \frac{3}{4}x} \\ = 4 + \frac{3}{16} [/tex]
According to the problem :
[tex]\sf{x – ( \frac{3}{4} + (4 + \frac{3}{16}x)) = 4} [/tex]
[tex]\sf{⇒x – ( \frac{3}{4}x + 4 + \frac{3}{16}x) = 4}[/tex]
[tex]\sf{⇒x – \frac{3}{4}x + – 4 – \frac{3}{16}x = 4} [/tex]
[tex]\sf{⇒x – \frac{3}{4}x – \frac{3}{16}x = 4 \times 4} [/tex]
[tex]\sf{⇒ \frac{16x – 12x – 3x}{16} = 8}[/tex]
[tex]\sf{⇒ \frac{x}{16} = 8} [/tex]
[tex]\sf{⇒x = 8 \times 16}[/tex]
[tex]\sf{⇒x = 128}[/tex]
Answer↷
Therefore, the total size of the whale is 128 inches .