Answer to Question #246733 in Algebra for korina

Question

A man died and left the following instructions for his fortune. Half to his wife, one-seventh of what was left to his son, two-thirds of what was left went to his butler, the man’s pet got the remaining 100,000 pesos. How much money did the man leave behind altogether?

Answer 1

Man leave A money altogether.

To wife: $A*\frac{1}{2}=\frac{A}{2}.$ Left $1-\frac{A}{2}=\frac{A}{2}.$

To son: $\frac{A}{2}*\frac{1}{7}=\frac{A}{14}.$ Left $\frac{A}{2}-\frac{A}{14}=\frac{3A}{7}.$

To butler: $\frac{3A}{7}*\frac{2}{3}=\frac{2}{7}.$ Left $\frac{3A}{7}-\frac{2A}{7}=\frac{A}{7}.$

To pet: $\frac{A}{7}=100000.$

Thus, $A=700000$.