Can you help me with a word problem?

Question

anonymous · Answer

Warren has 40 coins (all nickles, dimes, and quarters) worht $4.05.  He has 7 more nickels than dimes.  How many quarters does Warrn have?  I can't figure this out…..can you help?

anonymous · Answer

since nickels are worth 5 cents, dimes are worth 10 cents, and quarters are worth 25 cents, you can set up the following variables & equations: 
n + d + q = 40 (the total number of coins) 
5n + 10d + 25q = 405 (the value of each coin times the number he has of that coin = the total money he has) 
n = d + 7 (since his number of nickels = 7 MORE THAN his number of dimes) 

rearrange the equations with a bit of algebra and substitution... 
q = 40 - n - d 
q = 40 - (d+7) - d 
q = 33 - 2d 

5(d+7) + 10d + 25(33-2d) = 405 
5d + 35 + 10d + 825 - 50d = 405 
-35d = -455 
d = 13 

therefore n = 20 (since n = d+7) 
so 5(20) + 10(13) + 25q = 405 
100 + 130 + 25q = 405 
25q = 175 
q = 7