Please explain with complete step by step instructions.

#8)One type of lawn fertilizer consists of a mixture of nitrogen, phosphorus and potassium. An 80lb sample contains 8 move lbs of nitrogen and phosphorus than potassium. There is 16lb more potasssium than 5 times the amount of phosphorus. Let x be the amount of nitrogen, let y be the amount of phosphorus and let z be the amount potassium in the sample. Find the amount of each of the chemicals in the sample.

X = _____
y = _____
z = _____
(Hint: you must set up and solve a 3 by 3 systems of equations.)

I will assume that you meant "more" where you wrote "move"

The three equations you have to solve are
X + Y + Z = 80 (pounds)
X + Y - Z = 8
Z = 5Y + 16

The first two equations tell you right away that 2Z = 72, so Z = 36

The last equation tells you that 5Y = 20, so Y = 4.
X + 4 + 36 = 80, so X = 40

You're correct move is suppose to be more. Thank you so much for explaining this to me. It's very helpful.

To solve this problem, we will set up and solve a system of three equations in three variables.

Step 1: Assign variables to the unknowns.
Let x be the amount of nitrogen.
Let y be the amount of phosphorus.
Let z be the amount of potassium.

Step 2: Translate the given information into equations.
The problem states that the 80lb sample contains 8 more lbs of nitrogen and phosphorus than potassium. This can be written as:
x + y = z + 8 ----(Equation 1)

The problem also states that there is 16lbs more potassium than 5 times the amount of phosphorus. This can be written as:
z = 5y + 16 ----(Equation 2)

We know that the total weight of the sample is 80lbs, so the sum of the weights of the three chemicals must be equal to 80. This can be written as:
x + y + z = 80 ----(Equation 3)

Step 3: Solve the system of equations.
We have three equations with three unknowns (x, y, and z). We can solve this system of equations by using substitution, elimination, or matrix methods. In this case, we will use substitution.

From Equation 2, we can express z in terms of y:
z = 5y + 16

Substitute this value for z in Equations 1 and 3:
x + y = (5y + 16) + 8 ----(Equation 1')
x + y + (5y + 16) = 80 ----(Equation 3')

Simplifying Equation 1' and Equation 3':
x + 6y = 24 ----(Equation 1'')
x + 6y + 16 = 80 ----(Equation 3'')

Now, solve Equation 1'' for x:
x = 24 - 6y

Substitute this value for x in Equation 3'':
(24 - 6y) + 6y + 16 = 80
40 - 6y + 16 = 80
56 - 6y = 80
-6y = 24
y = -4

Now that we have the value of y, we can substitute it back into Equation 2 to find z:
z = 5y + 16
z = 5(-4) + 16
z = -20 + 16
z = -4

Finally, substitute the values of y and z into Equation 1 to find x:
x + y = z + 8
x + (-4) = -4 + 8
x - 4 = 4
x = 8

Step 4: Write the final answer.
The amount of each chemical in the sample is:
x = 8 lbs (nitrogen),
y = -4 lbs (phosphorus),
z = -4 lbs (potassium).

Note: The negative values for y and z indicate that the amount of phosphorus and potassium in the mixture is less than the amount of nitrogen.