SOLUTION: If Ruth is twice as old as Pat and in four years Ruth will be three times as old as Pat was three years ago, how old is each woman now?

Question 254357: If Ruth is twice as old as Pat and in four years Ruth will be three times as old as Pat was three years ago, how old is each woman now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If Ruth is twice as old as Pat and in four years Ruth will be three times as old as Pat was three years ago,
how old is each woman now?
:
Write an equation for each statement:
:
"If Ruth is twice as old as Pat"
r = 2p
:
"in four years Ruth will be three times as old as Pat was three years ago,"
r + 4 = 3(p - 3)
r + 4 = 3p - 9
r = 3p - 9 - 4
r = 3p - 13
:
Substitute 2p for r (from the 1st statement), find p
2p = 3p - 13
2p - 3p = -13
-p = -13
p = 13 yrs is Pat's present age
then, obviously:
r = 26 yrs is Ruth
:
:
See if that agrees with the 2nd statement:
"in four years Ruth will be three times as old as Pat was three years ago,"
26 + 4 = 3(13 - 3)
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