Answer:
Amount won : $3,000,000
Step-by-step explanation:
Let the amount won be =100 x
Amount spent on house :
[tex]\frac{4}{5} \ of \ 100 x = 80 x[/tex]
Remaining amount = 100x - 80x = 20x
Amount spent on yacht :
[tex]\frac{3}{4} \ of \ 20x = 15x[/tex]
Remaining amount = 20x - 15x = 5x
Amount spent on a trip :
[tex]\frac{2}{3} \ of \ 5x = \frac{10}{3}x[/tex]
Remaining amount =
[tex]5x - \frac{10}{3}x = \frac{15x -10x}{3} = \frac{5x}{3}[/tex]
This amount is given for charity :
[tex]\frac{5}{3}x[/tex]
But given :
Amount given to charity is 50000
Therefore ,
[tex]\frac{5}{3}x = 50000[/tex]
[tex]5x = 3 \times 50000\\\\5x = 150000\\\\x = 30000[/tex]
Therefore , the amount won on lottery is = 100x = 100 ( 30000) = 3,000,000
