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?

Question 161773: 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 ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let M = Matthew's age now
Let J = Jenny's age now
;
Their ages in 7 years:
(M+7) and (J+7)
:
Write an equation for each statement:
;
"Matthew is 3 times as old as Jenny."
M = 3J
:
In 7 years, he will be twice as old as she will be then."
(M+7) = 2(J+7)
Simplify equation
M + 7 = 2J + 14
M = 2J + 14 - 7
M = 2J + 7
:
How old is each now?
:
From the 1st equation; substitute 3J for M in the above equation
3J = 2J + 7
3J - 2J = 7
J = 7 yrs is Jenny's age now
:
Then from the 1st equation:
M = 3(7)
M = 21 yrs is Matthew's age now
;
:
Check solution in the statement:
"In 7 years, he will be twice as old as she will be then."
21 + 7 = 2(7+7)
:
:
Was this understandable? Did it make sense to you?

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