SOLUTION: doug dave and don are counting ducks down by the pond they are havinf a contest to see who can spot the most ducks. doug counts twice as many as dave. dave counts twice as many as

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Question 499621: doug dave and don are counting ducks down by the pond they are havinf a contest to see who can spot the most ducks. doug counts twice as many as dave. dave counts twice as many as don. together they spotted a total of 42 ducks. how many ducks did each boy spot
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = Doug's count of ducks, b = Dave's count, and c = Don's count.
a = 2b "Doug counts twice as many as Dave."
b = 2c "Dave counts twice as many as Don."
a+b+c = 42 ""Together they spotted a total of 42 ducks."
Rewrite the first equation:
a = 2b Replace b = 2c to get:
a = 2(2c)
a = 4c Now rewrite the second equation:
a+b+c = 42 Substitute a = 4c and b = 2c.
4c+2c+c = 42 Simplify.
7c = 42 Divide by 7.
c = 6 and...
b = 2(6)
b = 12 and...
a = 4c
a = 4(6)
a = 24.
Doug spotted 24 ducks.
Dave spotted 12 ducks.
Don spotted 6 ducks.