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?

Result

n =  780

Solution:

n1=429/(5+6)=39 n2=429/(5+9)=42914≐30.6429 n3=429/(6+9)=1435=28.6  n1∈N  j=5⋅ n1=5⋅ 39=195 r=6⋅ n1=6⋅ 39=234 f=9⋅ n1=9⋅ 39=351  n=j+r+f=195+234+351=780n_{1}=429 / (5+6)=39 \ \\ n_{2}=429 / (5+9)=\dfrac{ 429 }{ 14 } \doteq 30.6429 \ \\ n_{3}=429 / (6+9)=\dfrac{ 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

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