Question 658145
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.