Finding the right percentage

Question

Ella has 10% share because she invested 175 euro.
Chris has 10% share because he invested 175 euro.

Nathan invests 100 euro, how many shares will he get?

With some trial and error, I found the answer is 5.7142857143%.

5.7142857143 % of (175*10)

But I'm sure there has to be a better way of finding out the percentage for Nathan, how do I calculate this?

Answer 1

Unitary Method:

$175$ euros correspond to a $10\%$ share. $\\1$ euro -> $\frac{10}{175} \%$ share. $\\100$ euros -> $\frac{10}{175} \times 100\% = 5.714 \%$ share.

Answer 2

We know that the percentage share and euros invested are directly proportional. Let $P$ denote percentage and $E$ denote euros then the following equation is valid for some constant $k$

$$E=kP$$

With the existing data you can find $k$, and then use it to to get to the result.

Note: I used $E=kP$, because this way I could get $k>1$, however it is perfectly fine to use $P=kE$ and could be more suitable.

Answer 3

We can first find the total stock value as the $x$ such that $$ 0.10 \cdot x = 175 \text{ EUR} $$ This is solved by $x = 175 / 0.10 = 1750 \text{ EUR}$. Now we want to find the percentage $\alpha$ such that $$ \alpha \cdot 1750 \text{ EUR} = 100 \text{ EUR} $$ This is solved by $\alpha = 100 / 1750 = 0.057$, which is the same as $5.7\%$.

Answer 4

Let the total company value be $V$. We know that 10% of V is 175 €

Thus:

$ V \cdot \dfrac{10}{100} = 175 \Rightarrow V = 175 \times \dfrac{100}{10} = 1750$

Now we want to find $x$ the percentage of $V$ that 100 € represents.

Thus $V \cdot \dfrac{x}{100} = 100$

It should be trivial from here.