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?

KINGCASH Apr 19, 2021

#1**+2 **

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 the total buttons = T

If (2/3) of the buttons left were green, then (1/3) left were blue

So

Blue Buttons left = (1/3) (of what remains)

(3/7)T - 80 = (1/3) [ T - (2/5)T] simplify

(3/7)T - 80 = (1/3 ) (3/5)T

(3/7)T - 80 = (1/5)T

(3/7)T - (1/5)T = 80

[ 15 - 7 ] T / 35 = 80

8/35 T = 80

T = 80 (35/8) = 350 buttons at first

Proof

(2/5)(350) = 140 were given away

210 were left

140 were green

70 were blue

Total blue = 80 + 70 = (3/7)(350) =150

Total green = (4/7) (350) = 200

150 + 200 = 350

CPhill Apr 19, 2021