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:
[tex]\huge\fcolorbox{blue}{purple}{128}[/tex]
Step-by-step explanation:
[tex]\mathbb\pink{Mark \: as \: branliest \: plz}[/tex]
[tex]\Large\tt\fbox{✯Answer✯}[/tex]
[tex]\sf{Let\:the\:total\:size\:of\:the\:whale\:be\:x}[/tex]
[tex]\sf{Then,\:the\:size\:of\:the\:whale’s\: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}[/tex]
[tex] = 4 + \frac{3}{16} x[/tex]
[tex]\bf\green{According\:to\:the\:question:}[/tex]
[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 + 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]
[tex]\small\tt\pink{Answer: }[/tex]
The total size of the whale is 128 inches.