SOLUTION: Alice is as old as Betty and Christine together. Last year, Betty was twice as old a Christine. Two years hence, Alice will be twice as old as Christine. What are the ages of th

Question 603582: Alice is as old as Betty and Christine together. Last year, Betty was twice as old a Christine. Two years hence, Alice will be twice as old as Christine. What are the ages of the three girls?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Alice is as old as Betty and Christine together. Last year, Betty was twice as old a Christine.
Two years hence, Alice will be twice as old as Christine.
What are the ages of the three girls?
:
Write an equation for each statement
:
"Alice is as old as Betty and Christine together.
a = b + c
:
"Last year, Betty was twice as old a Christine."
b - 1 = 2(c-1)
b - 1 = 2c - 2
b = 2c - 2 + 1
b = 2c - 1
:
"Two years hence, Alice will be twice as old as Christine."
a + 2 = 2(c+2)
a + 2 = 2c + 4
a = 2c + 4 - 2
a = 2c + 2
:
the 1st equation
a = b + c
replace a with (2c+2). replace b with (2c-1)
2c + 2 = 2c - 1 + c
2 + 1 = c
c = 3 yrs old
then
a = 2(3) + 2
a = 8 yrs old
and
b = 2(3) - 1
b = 5 yrs old

What are the ages of the three girls? 8, 5, 3
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