SOLUTION: Abbey, Charles, and Monte are a sister and two brothers. Ten years ago, Abbey was twice as old as Charles was then. Three years ago, 4 times Monte's age was the same as 3 times Cha

Question 396654: Abbey, Charles, and Monte are a sister and two brothers. Ten years ago, Abbey was twice as old as Charles was then. Three years ago, 4 times Monte's age was the same as 3 times Charles' age at that time. In 15 years Abbey will be 8 years older than Monte is then. Find their ages now.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let {{a}}} = Abbey's age now
Let = Charles age now
Let = Monte's age now
= Abbey's age 10 years ago
= Charles age 10 years ago
= Monte's age 3 years ago
= Charles age 3 years ago
= Abbey's age in 15 years
= Mote's age in 15 years
-----------------------------
given:
(1)
(2)
(3)
--------------------
This is 3 equations and 3 unknowns, so it's solvable
Rewriting:
(1)
(1)
and
(2)
(2)
and
(3)
(3)
----------------
Multiply both sides of (3) by and
add (2) and (3)
(2)
(3)

------------------
Now multiply both sides of (1) by
and subtract (1) from last result

and, from (1):
(1)

and, from (3):
(3)

-----------
20 is Abbey's age now
15 is Charles age now
12 is Monte's age now
check answers:
(1)
(1)

and
(2)
(2)

and
(3)
(3)
OK
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