SOLUTION: matthew is 3 times as old as jenny. In 7 years he will be twice as old as she will be then. How old is each now?

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Question 128175: matthew is 3 times as old as jenny. In 7 years he will be twice as old as she will be then. How old is each now?
Answer by solver91311(24713) About Me  (Show Source):
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m is Matthew's age now. j is Jenny's age now.

m=3j because Matthew is three times as old as Jenny now.

In 7 years, Matthew will be m%2B7 years old, and Jenny will be j%2B7, and at that time:

m%2B7=2%28j%2B7%29 because Matthew will be twice as old as Jenny in 7 years.

But we know that m=3j so we can substitute this value into our last equation:

cartoon%28red%28m%29%2B7=2%28j%2B7%29%2Cred%283j%29%2B7=2%28j%2B7%29%29

3j%2B7=2%28j%2B7%29
3j%2B7=2j%2B14
3j-2j=14-7
j=7

So Jenny is 7 now, and Matthew is 3%2A7=21.

Check:
In seven years Jenny will be 14 and Matthew will be 28. 28 = 2 * 14. Answer checks.