In order to solve coin problems, or closely related problems, you should be able to:
Coin problems usually involve knowing how many coins and how much money someone has and trying to find out how many of each coin the person has. The same strategy used for solving coin problems can also be applied to other types of money or anything where there are several monetary values involved.
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
Usually coin problems involve two equations: one that describes how many coins there are and one that describes the amount of money.
that describes the number of coins is
since there are only nickels (N) and dimes (D) and there are 25 coins total.
the describes the amount of money is
since each nickel is worth 5 cents (0.05) and each dime is worth 10 cents (0.10) and the total amount of money is $1.65. To determine value we always multiply the worth of the item by how many of an item we have. Therefore, we are multiplying the value times the number of coins we have to come up with this equation.
To solve the equation
that describes the amount of money might look impossible because there are two variables. But this is where we will make use of the equation
that describes the number of coins.
that describes the number of coins can be re-written so that it is now
By subtracting N from both sides, we have a different version of the same equation.
Now that we have an expression
for D, we can substitute that back into the equation
that describes the amount of money.
Now we just need to solve the new equation.
This tells us that the number of nickels is equal to 17. Since we know the total number of coins is 25, that means the number of dimes is 8. Ken has 17 nickels and 8 dimes.