+58 2/5 of Sofia's postcards were equal to 7/9 to Jonas' postcards. After Sofia gave 2/7 of her postcards to Jonas, and Jonas received 6 postcards from his brother, Sofia had 5/11 of the total number of postcards. How many postcards did Jonas have in the end?
+128460 (2/5) S = ( 7/9) J
S = (5/2) (7/9) J
S = (35/ 18) J
If Sofia had 5/11 of the postcards at the end, then Jonas had 6/11 of them
The total cards = S + J + 6 = (35/18) J + J + 6 = (53/18)J + 6
Sofia gave Jonas (2/7)(35/18)J = (5/9)J
So.....the total number that Jonas had in the end = J + (5/9)J + 6 = (14/9)J + 6
So
[ (14/9)J + 6 ] 6
______________ = ______ cross-multiply
[ (53/18)J + 6] 11
6 [ (53/18)J + 6] = 11 [ (14/9)J + 6 ]
(53/3)J + 36 = (154/9)J + 66
(53/3)J - (154/9)J = 66 - 36
(5/9)J = 30
J = (30) (9/5) = 54
Jonas ended up wiith (14/9)(54) + 6 = 90 postcards
