Question

A pineapple was found to have two sets of opposing spirals formed by its leaves. The clockwise spiral has x leaves. The number of leaves in the counterclockwise direction is 8 more than that in the clockwise direction. These leaf numbers are consecutive numbers in the Fibonacci sequence.

Which equation is true for the number of leaves in the two spirals?


the quantity x plus 8/8=1.6

x/8=1.6

the quantity x plus 8/x=1.6

8/x=1.6

Answer 1

help please

Answer 2

ok that was wrong. fibonacci is
\[1,1,2,3,5,8,13,21,34,...\]

Answer 3

if one is 8 more than the other, the numbers must be 13 and 21

Answer 4

that is, x = 13, x + 8 = 21

Answer 5

now that we know the numbers, just need to check which answer is correct. for example
\[\frac{x+8}{8}=\frac{13+8}{8}=\frac{21}{8}\neq 1.6\] so that is out

Answer 6

\[\frac{x}{8}=\frac{13}{8}=1.625\] so that is out as well

Answer 7

actually i don't see any of these that are right

Answer 8

The 1.6 is an approximation to the golden ratio of (1+sqrt(5))/2=1.618....
which is supposed to be the ratio of successive Fibonacci numbers when n is high. For small values of n, i.e. the first few Fibonacci numbers, the value is only approximate, so 1.6 suffices.

So we assume (x+8)/x = 1.618....=1.6 approx.
You can then make the appropriate choice from the answers.