Jimenezmiranda
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Two years ago pete was three times as old as his cousin claire. Two years before that, pete was four times as old as claire. In how many years will the ratio of their ages be 2:1? Please explain or show work

Respuesta :

tramserran

Answer: 4

Step-by-step explanation:

Let P represent Pete's age today.  Let C represent Claire's age today.

2 years ago: P - 2 = 3(C - 2)  ⇒  P - 2 = 3C - 6   ⇒  P = 3C - 4

4 years ago: P - 4 = 4(C - 4)  ⇒  P - 4 = 4C - 16   ⇒  P = 4C - 12


Use substitution to solve the system above:

3C - 4 = 4C - 12

     - 4 = C - 12

       8 = C


Plug in the C-value above into one of the equations to solve for P:

P = 3C - 4

  = 3(8) - 4

  = 24 - 4

  = 20

So, Pete is 20 yrs old today and Claire is 8 years old today


When will Pete be twice as old as Claire?

20 + x = 2(8 + x)

20 + x = 16 + 2x

20       = 16 + x

4          = x

Their ages will have a 2:1 ratio in 4 years.  

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