SOLUTION: Diane is 29 years older than her daughter Amy. In 5 years Diane will be twice as old as Amy. How old are they now? I have tried different ways to set up the equation and I am

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Question 658145: Diane is 29 years older than her daughter Amy. In 5 years Diane will be twice as old as Amy. How old are they now?
I have tried different ways to set up the equation and I am not getting the correct answer. I need help to see how to determine what the equation is. I tried 2(x+29)=5 for Diane and x+5 for Amy. It does not work. Please help.
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = Diane's age and a = Amy's age. From the first sentence we have
d = a + 29
and from the second sentence we have:
d + 5 = 2*(a + 5)
Substituting the first equation into the second givs
(a + 29) + 5 = 2*(a + 5)
Expanding,
a + 34 = 2*a + 10
Subtract a from both sides:
a + 34 - a = 2*a + 10 - a
34 = a + 10
Reversing and subtracting 10 from each side:
a + 10 - 10 = 34 - 10
a = 24
So Amy is 24 and Diane is 53.