SOLUTION: Mike's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $5.40. The number of nickels is 2 short of being three times the sum of the number of d

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Question 28892: Mike's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $5.40. The number of nickels is 2 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?
Items I think I know about this problem
N+D+Q= 62
.05N+.10D+.25Q=$5.40
N= 3(D=Q)-2
Am I on the right track, and can I get some help solving.
Answer by venugopalramana(3286) About Me  (Show Source):
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Mike's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $5.40. The number of nickels is 2 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?
Items I think I know about this problem
N+D+Q= 62........I..........GOOD
.05N+.10D+.25Q=$5.40......VERY GOOD..TO REMOVE DECIMALS YOU MAY AS WELL WRITE THIS AS
5N+10D+25Q=540........................II
N= 3(D=Q)-2...I THINK YOU MEAN N=3(D+Q)-2.........III.......OK
Am I on the right track,...YA...GO AHEAD AND SOLVE
SUBSTITUTE FOR N FROM I IN II
5(62-D-Q)+10D+25Q=540
310-5D-5Q+10D+25Q=540
5D+20Q=230
D+4Q=46...............IV
SUBSTITUTE FOR N FROM I IN III
62-D-Q=3D+3Q-2
4D+4Q=64
D+Q=16...................V
EQN.IV-EQN.V...
3Q=30
Q=10
FROM EQN.V..........D=16-10=6
FROM EQN.I...........N=62-10-6=46
YOU CAN CHECK THE ANSWER...


and can I get some help solving.