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If I give my sister 5 dollars, then we will have the same amount of money. If instead she gives me 14 dollars, then I'll have twice as much money as she will have. How much money does she currently have (in dollars)?

 Feb 2, 2020
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Let  y  =  amount of money you now have.

Let  s  =  amount of money your sister now has.

 

If you give your sister 5 dollars, you will have 5 fewer dollars (y - 5) and she will have 5 more dollars (s + 5).

Since they are now equal:  y - 5  =  s + 5     --->     y  =  s + 10

 

If your sister gives you 14 dollars, you will now have 14 more dollars (y + 14) and she will have 14 fewer dollars (s - 14).

Since you will now have twice as much money as she has:     y + 14  =  2(s - 14)

     --->     y + 14  =  2s - 28     --->     y  =  2s - 42

 

Combining the equations:  s + 10  =  2s - 42     52  =  s

Since  s  =  52     --->     y  = 62

 Feb 2, 2020

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