SOLUTION: A coin collector has 31 dimes and nickels with a total face value of $2.40. (They are actually worth a lot more.) How many of each coin does she have?

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Question 505724: A coin collector has 31 dimes and nickels with a total face value of $2.40. (They are actually worth a lot more.) How many of each coin does she have?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
With money problems you have to keep track of the value of the coins and the number of coins.
n = number of nickels
5n = value
d = number of dimes
10d = value
.
n + d = 31
so
n = 31-d
.
5n + 10d = 240 cents (which is easier than fooling with decimals)
.
substitute n = 31-d
.
5(31-d) +10d = 240
155 -5d +10d = 240
5d = 240-155
5d = 85
d = 17
.
n = 31-17
n = 14
.
Check using the values.
.
5(14) = 70
10(17) = 170
70+170 = 240
Correct.
.
Answer: The collector has 14 nickels and 17 dimes.
.
Done.