SOLUTION: Hi I am trying to help my daughter with her math homework and I know the answer to the question but I am really not sure how I came up with it. Here is the question. Victor has

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Question 567635: Hi I am trying to help my daughter with her math homework and I know the answer to the question but I am really not sure how I came up with it. Here is the question.
Victor has 8 coins. He has 2 fewer dimes than nickels, and one more penny than nickels. How much money does he have?
In my head I figured out that there is going to be 1 dime, 3 nickels, and 4 pennies and that would of course equal 29 cents. Unfortunately we have to explain our answer and show the work and that is where I am stuck.
Thanks for your help!
Found 2 solutions by scott8148, Earlsdon:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
"Victor has 8 coins" ___ p + n + d = 8

"He has 2 fewer dimes than nickels" ___ d = n - 2

"one more penny than nickels" ___ p = n + 1

substituting ___ (n + 1) + n + (n - 2) = 8 ___ 3n - 1 = 8 ___ n = 3

use the value of n to find p and d

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Let D = the number of dimes, N = the number of nickels, and P = the number of pennies.
From the problem description, you can write:
1) D+N+P = 8 "Victor has 8 coins."
2) D = N-2 "He has 2 fewer dimes than nickels."
3) P = N+1 "...and one more penny than nickels."
Replace the D and the P in equation 1) with their equivalents from equations 2) and 3).
(N-2)+N+(N+1) = 8 Simplify this.
3N-1 = 8 Add 1 to both sides.
3N = 9 Now divide both sides by 3.
N = 3 and...
D = N-2
D = 3-2
D = 1 and...
P = N+1
P = 3+1
P = 4
So victor has 1 dime ($0.10), 3 nickels ($0.15), and 4 pennies ($0.04).
Add them together to get:
$0.29 or 29 cents.