A collection of dimes and nickels is worth 3.10. If there are 45 coins in all, how many of each kind of coins are there?

Answer 1

First, let's write out what we already know to be true:

Dime (D) = 0.10

Nickel (N) = 0.05

Next, let's create two equations for the question. Let's have D be the number of dimes and N be the number of nickels. We know some number of dimes plus some number of nickels equals 45 coins total:

D + N = 45

We can multiply the number of dimes and nickels by their value to figure out how much it is worth. We know that some number of dimes and some number of nickels is worth $3.10:

0.10D + 0.05N = 3.10

You can use substitution to find the value of D or N first:

D + N = 45 → subtract both sides by D

D - D + N = 45 - D

Becomes:

N = 45 - D

Now, plug this equation in to the second one to solve for D:

0.10D + 0.05N = 3.10

0.10D + 0.05(45 - D) = 3.10

0.10D + 2.25 - 0.05D = 3.10

0.05D + 2.25 = 3.10 → subtract 2.25 from both sides

Becomes:

0.05D = 0.85

0.05D/0.05 = 0.85/0.05

D = 17

Now we know there are 17 dimes! Let's plug that into the first equation to find out the number of nickels:

N + D = 45

N + 17 = 45

N = 28

There are 17 dimes and 28 nickels!