James has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have? Let n represent the number of nickles and q represent the number of quarters.

Question

James has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have? Let n represent the number of nickles and q represent the number of quarters.

Answer 1

add up the coins and their values:

n+q = 50
5n+25q = 1030
Now crank it out

Answer 2

Let's solve this problem step by step using algebra.

Step 1: Write out the information given in the problem.
James has a collection of new nickels and quarters.
He has a total of 50 coins worth $10.30.
Let n represent the number of nickels.
Let q represent the number of quarters.

Step 2: Write out the equations based on the information given.
We can write two equations based on the number of coins and their total value:
Equation 1: n + q = 50 (because James has a total of 50 coins)
Equation 2: 0.05n + 0.25q = 10.30 (because the total value is $10.30)

Step 3: Simplify and solve the system of equations.
We can solve the equations by using the substitution method or the elimination method. Let's use the elimination method.

To eliminate n from the equation, multiply Equation 1 by -0.05:
-0.05(n + q) = -0.05(50)
-0.05n - 0.05q = -2.50

Now add this equation to Equation 2:
0.05n + 0.25q + (-0.05n - 0.05q) = 10.30 + (-2.50)
0.20q = 7.80

Divide both sides of the equation by 0.20:
q = 7.80 / 0.20
q = 39

Now substitute the value of q back into Equation 1:
n + 39 = 50
n = 50 - 39
n = 11

So, James has 11 nickels (n) and 39 quarters (q).

Answer 3

To solve this problem, we can create a system of equations based on the given information.

Let's start by defining the variables:
n = number of nickels
q = number of quarters

We have two equations from the problem statement:

1. James has a total of 50 coins:
n + q = 50

2. The total value of the coins is $10.30:
0.05n + 0.25q = 10.30

Now, let's solve this system of equations using the substitution method.

From the first equation, we can express n in terms of q:
n = 50 - q

Now, substitute this expression for n in the second equation:
0.05(50 - q) + 0.25q = 10.30

Simplify the equation:
2.5 - 0.05q + 0.25q = 10.30
0.2q = 7.8
q = 7.8 / 0.2
q = 39

Now that we know the number of quarters (q = 39), we can substitute this value back into the first equation to find n:
n + 39 = 50
n = 50 - 39
n = 11

Therefore, James has 11 nickels (n = 11) and 39 quarters (q = 39).