A piggy bank contains $5.60 in nickels and dimes. The number of nickels is 8 less than 3 times the dimes. How many nickels and dimes are there in the piggy bank?

Let's break down the problem step-by-step:

Step 1: Set up the equations.
Let's assume the number of dimes in the piggy bank is "d" and the number of nickels is "n".

From the problem statement, we have two pieces of information:
1) The piggy bank contains $5.60. The value of each nickel is $0.05, and the value of each dime is $0.10. So, we can write the equation:
0.05n + 0.10d = 5.60

2) The number of nickels is 8 less than 3 times the number of dimes. We can write this as:
n = 3d - 8

Step 2: Solve the equations simultaneously.
Now, we can solve the equations simultaneously to find the values of "n" and "d".

Substitute the value of "n" from equation 2) into equation 1):
0.05(3d - 8) + 0.10d = 5.60

Simplifying the equation:
0.15d - 0.40 + 0.10d = 5.60
0.25d - 0.40 = 5.60
0.25d = 6.00
d = 6.00 / 0.25
d = 24

Now, substitute the value of "d" into equation 2) to find the value of "n":
n = 3(24) - 8
n = 72 - 8
n = 64

Therefore, there are 64 nickels and 24 dimes in the piggy bank.

To solve this problem, let's assign variables to the number of nickels and dimes in the piggy bank.

Let's say:
n = number of nickels
d = number of dimes

According to the given information, we can set up the following equations:

Equation 1: The value of the nickels (5 cents each) plus the value of the dimes (10 cents each) equals $5.60
0.05n + 0.10d = 5.60

Equation 2: The number of nickels is 8 less than 3 times the number of dimes
n = 3d - 8

Now, we have a system of two equations with two variables. To solve this system, we can use the substitution method or the elimination method. Let's use the substitution method:

Step 1: Substitute the value of n from Equation 2 into Equation 1.
0.05(3d - 8) + 0.10d = 5.60

Step 2: Simplify Equation 1 by distributing and combining like terms.
0.15d - 0.40 + 0.10d = 5.60
0.25d - 0.40 = 5.60

Step 3: Add 0.40 to both sides of the equation.
0.25d = 6.00

Step 4: Divide both sides of the equation by 0.25 to solve for d.
d = 6.00 / 0.25
d = 24

Step 5: Substitute the value of d back into Equation 2 to solve for n.
n = 3(24) - 8
n = 72 - 8
n = 64

So, there are 64 nickels and 24 dimes in the piggy bank.

N*.05+D*.1=5.60

N+8=3D

(3D-8).05+ .1D=5.60
solve for D first.