SOLUTION: The sum of Joe's age and Mary's age is 60 years. Ten years ago, Joe was 3 times as old as Mary was then. How old is each now?

Question 132068: The sum of Joe's age and Mary's age is 60 years. Ten years ago, Joe was 3 times as old as Mary was then. How old is each now?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Joe is x years old
Mary is y years old
We are given that

Ten years ago, Joe was x - 10 years old and Mary was y - 10 years old.
We are given that

Put the second relationship into standard form ()

Now we have two equations in standard form:

Multiply the second equation by -1:

Add the first equation to the second, term by term:

Divide by the coefficient on y:

Therefore Mary is 20 years old now. That means that Joe is 40 years old now (60 - 20). Ten years ago, Joe would have been 30 and Mary would have been 10, and 30 is 3 times 10. Answer checks.
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