SOLUTION: if Juan gives Pedro 10 pesos. Pedro will have three times as much money as Juan. if Pedro gives Juan 10 pesos, Juan will have twice as much money as Pedro. how much did each have?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: if Juan gives Pedro 10 pesos. Pedro will have three times as much money as Juan. if Pedro gives Juan 10 pesos, Juan will have twice as much money as Pedro. how much did each have?       Log On


   

Question 898627: if Juan gives Pedro 10 pesos. Pedro will have three times as much money as Juan. if Pedro gives Juan 10 pesos, Juan will have twice as much money as Pedro. how much did each have?
Answer by Edwin McCravy(20060) About Me  (Show Source):
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if Juan gives Pedro 10 pesos. Pedro will have three times as much money as Juan. if Pedro gives Juan 10 pesos, Juan will have twice as much money as Pedro. how much did each have? 
We begin with Pedro having P peson and Juan having J pesos.

Juan gives Pedro 10 pesos. 
Juan now has J-10 and Pedro has P+10

Pedro will have three times as much money as Juan. 
     P+10 = 3(J-10)
     P+10 = 3J-30
(1)     P = 3J-40

We begin again with Pedro having P peson and Juan having J pesos.

Pedro gives Juan 10 pesos, 
Pedro has P-10 and Juan has J+10

Juan will have twice as much money as Pedro.
     J+10 = 2(P-10)
     J+10 = 2P-20
(2)     J = 2P-30

Solve (1) and (2)

        P = 3J-40
        P = 3(2P-30)-40
        P = 6P-90-40
        P = 6P-130
      -5P = -130
        P = 26 pesos

        J = 2P-30
        J = 2(26)-30
        J = 52-30  
        J = 22 pesos

Checking:


We begin with Pedro having 26 peson and Juan having 22 pesos.



Juan gives Pedro 10 pesos. 


Juan now has 22-10=12 and Pedro has 26+10=36 



Pedro will have three times as much money as Juan. 


That checks, since 36 is 3 times 12




Pedro gives Juan 10 pesos, 


Pedro has 26-10=16 and Juan has 22+10=32



Juan will have twice as much money as Pedro.


That checks, since 32 is 2 times 16

Edwin