Temples $\propto$ Flowers ?!!

Algebra Level 2

You visit a shrine that has three temples in a magical pond. Before you visit a temple you have to swim in the pond. Each time you swim in the pond, the number of flowers you are carrying triples. You place equal number of flowers at each temple you visit.

At the end, you have no flowers; what is the least number of flowers you could have started with?

Give your answer as : [the number of flowers you started with] + [the number of flowers you leave at each temple]

Remember:

You start with a positive number of flowers and you place a whole number of flowers each time.
The route is as follows $\to$ pond--temple1--pond--temple2--pond--temple3

35 39 40 41 42 36

2 solutions

Syed Hamza Khalid
Nov 13, 2017

$\large \text{ The question states the sum of } x \text{ and } y \color{#3D99F6} \implies 27 + 13 = \color{#D61F06} 40$

Md Mehedi Hasan
Nov 11, 2017

Let, the number of flowers I started with is $x$ and the number of flowers I leave at each temple is $y$

we can calculate it by this diagram,

$\begin{matrix} start & pond & Temple 1 & pond & Temple2 & pond & Temple3 & finally \\ x & 3x & 3x-y & 3(3x-y) & 3(3x-y)-y & 3(3(3x-y)-y) & 3(3(3x-y)-y)-y & 0 \end{matrix}$

Then we can write, $3(3(3x-y)-y)-y=0$

Calculating we get, $x=\frac{13y}{27}$

For $x$ is a positive integer and least number, $y=27$ Then we get $x=13$

Then the answer is $27+13=\boxed{40}$

Temples ∝ \propto ∝ Flowers ?!!

2 solutions

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Temples $\propto$ Flowers ?!!