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# Help with math

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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?

Jun 6, 2021

#1
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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?

(3/7)  are blue    (4/7)  are green....let N  be  the total

No.remaining  = blue remaining + green remaining

(3/5)N =   [(3/7)N -80 ]  +  (2/3) (N - (2/5)N)        simplify

(3/5)N  = (3/7)N  - 80  + (2/3)N  - (4/15)N

(3/5)N  =  (3/7)N  - 80  + (10/15)N - (4/15)N

(3/5)N  = (3/7)N - 80  +    (2/5)N

80 = (3/7)N   + (2/5)N - (3/5)N

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

80  =  (15/35)  - (7/35)N

80  =  (8/35) N

N = 80 (35/8)   =     350   Jun 6, 2021