Ryan had some blue and green buttons. 3/7 of the buttons are blue and the rest were green. He gave away 2/5 of his buttons. 80 of the buttons given away were blue. 2/3 of the buttons left were green. How many buttons did Ryan have altogether at first?
Let x be no of buttons Ryan had
Then
No of Blue buttons = 3/7x * = 3x/7
=> No of Green Buttons = x - 3x/7 = 4x/7 -(3)
Ryan gave away buttons = 2/5x * = 2x/5
Buttons Left = x - 2x/5 = 3x/5
Given away button = 2x/5
Blue given away = 80
Green give away = 2x/5 - 80 -(2)
Green button left = 2/3x(3x/5) = 2x/5 -(1)
Green Button Left + Given button Givrn away = Total Green Button
So (1),(2),(3) we have
2x/5 + 2x/5 - 8o = 4x/7
4x/5 - 4x/7 = 80
28x-20x/35 = 80
x = 10×35
x = 350
Total Buttons Ryan had = 350
