Question 170225: Slick jim won the lottery.he spent Two thirds of his winnings on a very posh house.he spent two thirds of what he had left on a luxury yacht. Then he spent two thirds of what he had left on a hot air balloon. He spent his last £20000 on a flashy car. How much did Slick Jim win on the lottery? many thanks,dj.
Found 2 solutions by ptaylor, maali40:
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let w=Slick Jim's initial winnings
1. He spent (2/3)w on a posh house and had (w-(2/3)w)=(1/3)w left
2. He spent (2/3)*(1/3)w=(2/9)w on a luxury yacht and had ((1/3)w-(2/9)w)=
(3/9)w-(2/9)w=(1/9)w left
3. He spent (2/3)*(1/9)w=(2/27)w on a hot air baloon and had ((1/9)w-(2/27)w)=
(3/27)w-(2/27)w=(1/27)w left and we are told that this equals £20000, so our equation to solve is:
(1/27)w=£20000 multiply each term by 27
w=£540,000-------------------------------------his winnings
CK
(2/3)*540,000=360,000; 540,000-360,000=180,000
(2/3)*180,000=120,000; 180,000-120,000=60,000
(2/3)*60,000=40,000; 60,000-40,000=20,000
20,000=20,000
Hope this helps---ptaylor
Answer by maali40(13)  (Show Source):
You can put this solution on YOUR website! W pounds ='s winnings L='s 200000 2/3*W * (the sum of parts that follow as j=0 to 2 of (1/3)^j) = W-L=2/3*W*((1/3)^3-1)/(1/3-1)=52/54*W =W-200000. Therefore w=200000/27
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