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# Fractions

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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?

Jun 19, 2021

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(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   Jun 19, 2021