SOLUTION: Ruth is twice as old as Pat. In 4 years, Ruth will be three times as old as Pat was 3 years ago. How old is each now?

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Question 206130: Ruth is twice as old as Pat. In 4 years, Ruth will be three times as old as Pat was 3 years ago. How old is each now?
Answer by Marth(57) About Me  (Show Source):
You can put this solution on YOUR website!
Right now, "Ruth is twice as old as Pat."
let x = Pat's age
2x = Ruth's age
"In 4 years, Ruth will be three times as old as Pat was 3 years ago."
2x%2B4 is Ruth's age in 4 years. x-3 is Pat's age 3 years ago.
Because Ruth will be three times as old, 2x%2B4+=+3%28x-3%29
Solve.
2x%2B4+=+3%28x-3%29
2x%2B4+=+3x-9
Subtract 2x and add 9 to both sides
13+=+x
_______
Since x = Pat's age and 2x = Ruth's age,
Pat is 13 now.
Ruth is 26 now.