SOLUTION: Tiarn is x years old. Her friend Rose is ten less than twice her age. Another friend, Pam is five years younger than Rose. The sum of Tiarn, Rose and Pam’s ages is fifty. Write a

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Question 1155908: Tiarn is x years old. Her friend Rose is ten less than twice her age. Another friend, Pam is five years younger than Rose. The sum of Tiarn, Rose and Pam’s ages is fifty. Write an equation and solve it to find the ages of all the people.
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Tian is x years old.

Rose is (2x-10) years old.

Pam is ((2x-10)-5) = (2x-15) years old.


The total of their ages is


    x + (2x-10) + (2x-15) = 50.


Simplify ans solve


    5x - 25 = 50

    5x      = 50 + 25 = 75

     x                = 75/5 = 15.


You complete from this point.

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Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Tiarn is x years old.
T = x
Her friend Rose is ten less than twice her (Tiarn's) age.
R = 2T - 10
Substitute x for Tiarn's age T
R = 2x - 10
Another friend, Pam is five years younger than Rose.
P = R - 5
Substitute 2x - 10 for R in that.
P = 2x - 10 - 5
Combine the -10 - 5 as -15
P = 2x - 15
The sum of Tiarn, Rose and Pam’s ages is fifty.
T + R + P = 50
Write an equation.....
In T + R + P = 50,
Substitute x for Tiarn's age T.
Go back to R = 2x - 10 and substitute 2x - 19 for R
Go back to P = 2x - 15 and substitute 2x - 15 for P

x + 2x - 10 + 2x - 15 = 50
.....and solve it to find the ages of all the people.
Combine the like terms on the left:

5x - 25 = 50
     5x = 75
      x = 15

      T = x
      T = 15, so Tiarn is 15

      R = 2x - 10
      R = 2(15) - 10
      R = 30 - 10
      R = 20, so Rose is 20
      
      P = 2x - 15
      P = 2(15) - 15
      P = 30 - 15
      P = 15. so Pam is 15, same age as Tiarn 
      
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Checking:

Tiarn is x years old. 

Tiarn is 15

Her friend Rose is ten less than twice her age. 

Rose is 20.  10 less than twice 15 is 10 less than 30, which is 20.

Another friend, Pam is five years younger than Rose. 

Pam is 15.  Rose is 20.  15 is five years younger than Rose. 

The sum of Tiarn, Rose and Pam’s ages is fifty. 

15 + 20 + 15 = 50.   So the answers are correct.

Edwin