SOLUTION: There are a total of 23 nickels and dimes. Together, they make $1.95. How many of the coins are nickles, and how many are dimes?

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: There are a total of 23 nickels and dimes. Together, they make $1.95. How many of the coins are nickles, and how many are dimes?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 938885: There are a total of 23 nickels and dimes. Together, they make $1.95. How many of the coins are nickles, and how many are dimes?
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!
Method 1:
Solve using a single equation:

Let d=number of nickels (worth 10 cents each)
then 23-d = number of nickels (worth 5 cents each)

We have total value
10d + 5(23-d) = 195 cents

Distribute and group like terms
10d + 115 -5d = 195
5d = 195-115
5d = 80
d=16
Answer: So there are 16 dimes and 23-16=7 nickels.
Check: 16(10)+7(5)=160+35=195 cents = $1.95 checks.


Method 2: (can be done mentally)
Assume all coins are dimes, then value = 23*10 = 230 cents.
There is an excess of 230-195=35 cents.
So number of nickels = 35 cents / (10-5) cents = 7
Number of dimes = 23-7 = 16 as as before.