SOLUTION: A collection of 40 dimes and nickels is worth $2.90. How many nickels are there?

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: A collection of 40 dimes and nickels is worth $2.90. How many nickels are there?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 108480This question is from textbook Algebra Structure and Method
: A collection of 40 dimes and nickels is worth $2.90. How many nickels are there? This question is from textbook Algebra Structure and Method

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
These kind of problems require that you deal both with the number of coins and their value. Knowing that there are 40 total coins allows us to write:
:
d+%2B+n=40
:
Knowing that there are 10 cents in each dime, 5 cents in each nickel, and a total of 290 cents ($2.90) in value for the 40 coins, we can write:
:
10d%2B5n=290
:
but since d=40-n, we can substitute:
:
10%2840-n%29%2B5n+=+290
400-10n%2B5n=290
-5n=-110
n=22
:
Meaning that there are 22 nickels worth $1.10.
:
To check your answer, note that there are 40-22=18 dimes. And 18 dimes are worth, $1.80. 1.80+%2B+1.10+=+2.90