# a collection of 41 nickles and dimes has a value of 3.35. how many nickles and how many dimes are there?

Let's use the variable n to represent the NUMBER of nickels and the variable d to represent the NUMBER of dimes.

Since we know there is a total of 41 coins, we can write: n + d = 41

Then since each nickel is worth 5 cents or $0.05 and each dime is worth 10 cents or 0.10, we can write: 0.05n + 0.10d =$3.35

Now we can use substitution to solve these two equations with two unknowns.

From the first equation, we can write: d = 41 - n

Then substitute this expression for d into the second equation and solve using the distributive property and inverses:

0.05n + 0.10d = \$3.35

0.05n + 0.10(41 - n) = 3.35

0.05n + 4.1 - 0.10n = 3.35

-0.05n + 4.1 = 3.35

-0.05n + 4.1 - 4.1 = 3.35 - 4.1

-0.05n = -0.75

n = 15

There are 15 nickels . Since there are 41 coins in all, there will be 26 dimes.

em ENEM