SOLUTION: I have 19 coins that are worth a total of $1.10. If they consist only of dimes and nickels, then how many nickels do I have?

Question 251281: I have 19 coins that are worth a total of $1.10. If they consist only of dimes and nickels, then how many nickels do I have?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
With coin problems, you typically will have a statement regarding the number of coins and another that addresses their value. You have to keep the two things (count and value) separate.
d = number of dimes
10d = value of dimes
n = number of nickels
5n = value of nickels
.
d + n = 19 (given)
10d + 5n = 110 cents (given)
.
n = 19-d = number of nickels
.
Substitute:
10d + 5(19-d) = 110
Solve
10d + 95 - 5d = 110
5d = 15
d = 3 = number of dimes
19-3 = 16 = number of nickels
.
Check by substituting.
10(3) = 30 cents in dimes
5(16) = 80 cents in nickels
total = 110 cents
.
Checks.
So we conclude:
The number of dimes is 3; the number of nickels is 16.
.
Done
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