I need help with these problems:

1) A vending machine takes only nickels and dimes. There are 5 times as many dimes as nickels in the machine. The face value of the coins is $4.40. How many of each coin are in the machine?

2) A vending machine takes only nickels and dimes. At the end of the day there were 3 times as many nickels as dimes and a total of $25. How much of each coin were in the machine?

I know that there should be two equations for each problem. But I just don't know what the equations will be.
Please help.

1) D=5N

.10D+.05N=4.40

2) N=3D
you do the value equation as I did above.

Thank You.

Let's break down each problem and create the equations step-by-step:

Problem 1)

Let's represent the number of nickels as "N" and the number of dimes as "D".

We are given two pieces of information:
1) There are 5 times as many dimes as nickels: D = 5N
2) The total value of the coins is $4.40: 0.05N + 0.10D = 4.40

To solve this system of equations, we can substitute the value of "D" from the first equation into the second equation.

0.05N + 0.10(5N) = 4.40
0.05N + 0.50N = 4.40
0.55N = 4.40
N = 4.40 / 0.55
N = 8

Now, substitute the value of "N" back into the first equation to find the value of "D":

D = 5N
D = 5(8)
D = 40

Therefore, there are 8 nickels and 40 dimes in the vending machine.

Problem 2)

Again, let's represent the number of nickels as "N" and the number of dimes as "D".

We are given two pieces of information:
1) There are 3 times as many nickels as dimes: N = 3D
2) The total value of the coins is $25: 0.05N + 0.10D = 25

To solve this system of equations, we can substitute the value of "N" from the first equation into the second equation.

0.05(3D) + 0.10D = 25
0.15D + 0.10D = 25
0.25D = 25
D = 25 / 0.25
D = 100

Now, substitute the value of "D" back into the first equation to find the value of "N":

N = 3D
N = 3(100)
N = 300

Therefore, there are 300 nickels and 100 dimes in the vending machine.

In summary:
1) There are 8 nickels and 40 dimes in the machine.
2) There are 300 nickels and 100 dimes in the machine.

Sure! Let's break down each problem and set up the equations.

1) First problem: A vending machine takes only nickels and dimes. There are 5 times as many dimes as nickels in the machine. The face value of the coins is $4.40. How many of each coin are in the machine?

Let's assume the number of nickels is N and the number of dimes is D.

We are given that there are 5 times as many dimes as nickels, so we can write the equation: D = 5N (Equation 1).

We are also given that the total face value of the coins is $4.40. The value of a nickel is $0.05, and the value of a dime is $0.10. So we can write the equation: 0.05N + 0.10D = 4.40 (Equation 2).

These are the two equations for this problem:
Equation 1: D = 5N
Equation 2: 0.05N + 0.10D = 4.40

Now, let's move on to the second problem.

2) Second problem: A vending machine takes only nickels and dimes. At the end of the day, there were 3 times as many nickels as dimes and a total of $25. How much of each coin was in the machine?

Again, let's assume the number of nickels is N and the number of dimes is D.

We are given that there are 3 times as many nickels as dimes, so we can write the equation: N = 3D (Equation 3).

We are also given that the total value of the coins is $25. Using the same values as before, we can write the equation: 0.05N + 0.10D = 25 (Equation 4).

These are the two equations for this problem:
Equation 3: N = 3D
Equation 4: 0.05N + 0.10D = 25

Now that we have set up the equations, we can solve them using various methods such as substitution or elimination to find the values of N and D for each problem.