Lucas has 18 coins. there are three times as many pennies as dimes and twice as many nickels as dimes. the number of each coin is divisible by 3 and the number of nickels is also divisible by 2. how many of each coin does lucas have?

18=p+d+n, 3p=d, 2n=d
The lowest number that is divisible by 3&2 is 6 so, there is 6 nickels.
There is 6 nickels and there is half of that in dimes, 3 dimes.
There is three times the amount of pennies of dimes. 3*3=9. There is 9 pennies.
6 nickels + 3 dimes + 9 pennies= 18 coins

Ais the correct answer