Question 1205102
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x = number of marbles he started with
(3/5)x = number of marbles given away
(2/5)x = number of marbles he keeps
(2/5)x+20 = amount after buying 20 more marbles



(2/5)x+20 = 100
(2/5)x = 100-20
(2/5)x = 80
x = 80*(5/2)
x = <font color=red size=4>200</font>



Another way to solve
(2/5)x+20 = 100
5*( (2/5)x+20 ) = 5*100
5*(2/5)x + 5*20 = 500
2x + 100 = 500
2x = 500 - 100
2x = 400
x = 400/2
x = <font color=red size=4>200</font>



Check:
He started with <font color=red>200</font> marbles.
3/5 of which is (3/5)*200 = 0.6*200 = 120
He gives away 120 marbles and keeps 200-120 = 80. Note how (2/5)*200 = 0.4*200 = 80.
Then he buys 20 marbles to get 80+20 = 100 total at the end. We have confirmed the answer.


Another way to check:
(2/5)x+20 = 100
(2/5)*<font color=red>200</font>+20 = 100
0.4*200+20 = 100
80+20 = 100
100 = 100
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