SOLUTION: lucas has 18 coins, pennies, nickels, and dimes in his pocket. there are three times as many pennies as dimes and twice as many nickels as dimes. the number of each is divisible

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Question 936957: lucas has 18 coins, pennies, nickels, and dimes in his pocket. there are three times as many pennies as dimes and twice as many nickels as dimes. the number of each is divisible by 3, and the number of nickels is also divisible by 2. how many of each does lucas have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +p+%2B+n+%2B+d++=+18+
(2) +p+=+3d+
(3) +n+=+2d+
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Substitute (2) and (3) into (1)
(1) +3d+%2B+2d+%2B+d+=+18+
(1) +6d+=+18+
(1) +d+=+3+
----------------
(2) +p+=+3d+
(2) +p+=+3%2A3+
(2) +p+=+9+
----------------
(3) +n+=+2d+
(3) +n+=+2%2A3+
(3) +n+=+6+
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There are 9 pennies, 6 nickels, and 3 dimes
check:
(1) +p+%2B+n+%2B+d++=+18+
(1) +9+%2B+6+%2B+3++=+18+
(1) +18+=+18+
OK