can someone help explain how to do this?

allen has nickels dimes and quarters in his pocket. the number of nickels is 1 more than twice the number of quarters. the number of dimes is 1 less than the number of quarters. if the value of change in his pocket is 85 cents, how many of each coin does he have?

number of quarters = x

number of nickels = 2x+1
number of dimes = x-1

now use the "value" of those coins to get
25x + 5(2x+1) + 10(x-1) = 85

should be pretty easy to solve

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

Let's define the following variables:
N = number of nickels
D = number of dimes
Q = number of quarters

From the problem, we know the following relationships:
1) The number of nickels is 1 more than twice the number of quarters: N = 2Q + 1
2) The number of dimes is 1 less than the number of quarters: D = Q - 1
3) The value of all the coins is 85 cents: 5N + 10D + 25Q = 85

Now, we can solve this system of equations to find the values of N, D, and Q.

Substitute the value of N from equation 1 into equation 3:
5(2Q + 1) + 10D + 25Q = 85
10Q + 5 + 10D + 25Q = 85
35Q + 10D = 80 (dividing the equation by 5)

Next, substitute the value of D from equation 2 into the equation above:
35Q + 10(Q - 1) = 80
35Q + 10Q - 10 = 80
45Q = 90
Q = 2

Now that we know the value of Q, we can find the values of N and D.

Substitute Q = 2 into equation 2:
D = 2 - 1
D = 1

Substitute Q = 2 into equation 1:
N = 2(2) + 1
N = 5

Therefore, Allen has 5 nickels, 1 dime, and 2 quarters.

To solve this problem, we can set up a system of equations using the information given in the problem.

Let's denote the number of nickels as N, the number of dimes as D, and the number of quarters as Q.

From the problem, we have three pieces of information:

1. "The number of nickels is 1 more than twice the number of quarters."
Mathematically, this can be written as: N = 2Q + 1.

2. "The number of dimes is 1 less than the number of quarters."
Mathematically, this can be written as: D = Q - 1.

3. "The value of change in his pocket is 85 cents."
The value of each coin can be represented as follows:
- The value of a nickel is 5 cents.
- The value of a dime is 10 cents.
- The value of a quarter is 25 cents.

We can create an equation based on the total value of each coin:
5N + 10D + 25Q = 85.

Now we have a system of equations:
N = 2Q + 1 (Equation 1)
D = Q - 1 (Equation 2)
5N + 10D + 25Q = 85 (Equation 3)

To solve this system, we can use a method called substitution or elimination.

Let's use substitution:
From Equation 1, we can say that N = 2Q + 1.
Substitute this value for N in Equation 3:
5(2Q + 1) + 10D + 25Q = 85.

Expand and simplify:
10Q + 5 + 10D + 25Q = 85.
35Q + 10D = 80.
7Q + 2D = 16 (Divide both sides by 5 to simplify).

Now, let's use substitution again:
From Equation 2, we can say that D = Q - 1.
Substitute this value for D in the previous equation:
7Q + 2(Q - 1) = 16.

Expand and simplify:
7Q + 2Q - 2 = 16.
9Q = 18.
Q = 2.

Now that we have the value of Q, we can substitute it back into Equation 2:
D = 2 - 1 = 1.

Similarly, substitute Q's value into Equation 1:
N = 2(2) + 1 = 5.

So, Allen has 5 nickels, 1 dime, and 2 quarters in his pocket.