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Ally and Billy had $480. Ally gave 2/5 of her money to Billy. Billy then gave 3/7 of his total amount to Ally. They then had the same amount of money. How much money did Ally have at first?

 Sep 30, 2021
 #1
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Initially

a + b = 480      or   b = 480-a

 

then

(a-2/5a)  + (b + 2/5 a  ) 3/7    =    (b+2/5 a) 4/7       (b+2/5a) is the amount b has after a gives him 2/5....then he gives back 3/7 leaving b with 4/7

3/7 b + 6/35 a      +   3/5 a    =    4/7 b + 8/35 a

19/35 a = 1/7 b                now sub in the red equation

19/35 a = 1/7 (480-a)

24/35 a  = 480/7

a = 100 dollars at first

 Sep 30, 2021

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