Kaden and John had some marbles. John gave away 3/5 as many marbles as Kaden and was left with 4 fewer marbles than the marbles he gave away. Kaden has 2/5 as many marbles left as John. The difference between the number of marbles they had in the end was 21. How many marbles did Kaden have at first?
+128408 Call the number of marbles that Kaden gave away = G
Call the number of marbles that John gave away = (3/5)G
The number of marbles that John ends up with = (3/5)G - 4
The number of marbles that Kaden ends up with = (2/5) [ (3/5)G - 4]
So
(3/5)G - 4 - (2/5) [ (3/5)G - 4 ] = 21 simplify
(3/5)G - (6/25)G - 4 + 8/5 = 21
(15/25)G - (6/25)G - 4 + 8/5 = 21
(9/25)G = 21 + 4 -8/5
(9/25)G = 117/5
G = (117/5) ( 25/9) = 65
John must have started with (3/5)G + (3/5)G - 4 = (6/5)(65) - 4 = 74
Kaden must have started with G + (2/5)[ (3/5)G - 4] = 65+ (2/5) [ (3/5)(65) - 4 ] =
65 + (2/5) [ 35] =
65 + 14 =
79
Proof
John started with 74 and gave away (3/5)(65) = 39
So he had 35 left
Kaden started with 79 and gave away 65
So....he had 14 left
And
35 -14 = 21
