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Question 157309: A collecton of 197 coins consists of nickels, dimes, and quarters. The number if dimes is 2 more than one-third the number of nickels, and the number of quarters is three times the number of dimes. How many dimes are there?


I did some work but I cant figure it out
D+N+Q=197
D=1/3N+2 3D=N+6
Q=3D
: A collecton of 197 coins consists of nickels, dimes, and quarters. The number if dimes is 2 more than one-third the number of nickels, and the number of quarters is three times the number of dimes. How many dimes are there?


I did some work but I cant figure it out
D+N+Q=197
D=1/3N+2 3D=N+6
Q=3D

Answer by jim_thompson5910(9368) About Me  (Show Source):
You can put this solution on YOUR website!
D+N+Q=197 Start with the first equation


(1/3)N+2+N+3D=197 Plug in D=(1/3)N+2 and Q=3D


(1/3)N+2+N+3((1/3)N+2)=197 Plug in D=(1/3)N+2


(1/3)N+2+N+3((1/3)N)+3(2)=197 Distribute


(1/3)N+2+N+N+6=197 Multiply


(1/3)N+2N+8=197 Combine like terms.


N+6N+24=591 Multiply EVERY term by the LCD 3 to clear out the fractions.


7N+24=591 Combine like terms.


From here you have a simple linear equation. Once you have N, plug this into the second equation to get D. Finally, plug D into the third equation to get Q. Let me know if you need any further help.


Note: you should get D=29, N=81, and Q=87 as an answer.