SOLUTION: The sum of Anne's, Bert's and Chris's age is 60. Anne is older than Bert by the same number of years that Bert is older than Chris. When Bert is as old as Anne is now, Anne will b

Question 98055: The sum of Anne's, Bert's and Chris's age is 60. Anne is older than Bert by the same number of years that Bert is older than Chris. When Bert is as old as Anne is now, Anne will be three times as old as Chris is now. Set up the equations to solve this problem.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of Anne's, Bert's and Chris's age is 60.
a + b + c = 60
:
Anne is older than Bert by the same number of years that Bert is older than Chris.
a - b = b - c = x
Let x = difference between a & b, and b & c
Then:
b = a-x
c = a-2x
When Bert is as old as Anne is now, Anne will be three times as old as Chris is now.
b + x = a (now)
then find a in terms of x:
(a + x) = 3c
a + x = 3(a-2x); substituted (a-2x) for c
a + x = 3a - 6x
a - 3a = -6x - x
-2a = -7x
2a = 7x
a = 3.5x
:
a + b + c = 60
Substitute for b and c,
a + (a-x) + (a-2x) = 60
3a - 3x = 60
a - x = 20
:
3.5x - x = 20; substituted 3.5x for a, find x
2.5x = 20
x = 20/2.5
x = 8 is the difference
:
a = 3.5x; find a from knowing x
a = 3.5(8)
a = 28 yrs old, then, b = 20 yrs old, and, c = 12 yrs old
:
Check solution from the statement:
"When Bert is as old as Anne is now, Anne will be three times as old as Chris is now.
When B is 28(A's age now), A(28+8) = 3(12(C's age now))
:
Hope this made sense.
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