Collection of stamps

Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?

Correct result:

n =  780

Solution:

$$\begin{gathered} n_1=429\mathrm{/}(5+6)=39 \\ {n}_2=429\mathrm{/}(5+9)={\displaystyle \frac{429}{14}}\doteq 30.6429 \\ {n}_3=429\mathrm{/}(6+9)={\displaystyle \frac{143}{5}}=28.6 \\ {n}_1\in N \\ j=5\cdot n_1=5\cdot 39=195 \\ r=6\cdot n_1=6\cdot 39=234 \\ f=9\cdot n_1=9\cdot 39=351 \\ n=j+r+f=195+234+351=780 \end{gathered}$$

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