Question

a bank contains 21 coins, consisting of nickels and dimes. how many coins of each kind does it contain if their total value is $1.65?

Answer 1

There are 9 Nickels & 12 Dimes.

Explanation:

Let N = the number of nickels

Let D = the number of dimes

Each nickel is worth 0.05

Each dime is worth 0.10

So let's write some equations.

0.05N + 0.10D = 1.65

N + D = 21

We can solve by substitution.

Rewrite that 2nd equation.

N = 21-D

Now substitute that ^^^ equation into the first equation.

0.05(21-D) + 0.10D = 1.65

1.05-0.05D + 0.10D = 1.65

Combine like terms.

0.05D = 0.6

Divide both sides by 0.05

D = 12

There are 12 Dimes.

N + D = 21

N + 12 = 21

N = 21-12

N = 9

There are 9 Nickels & 12 Dimes.

Check that our answer is correct.

9(.05) + 12(.10) = 0.45 + 1.20 = 1.65