Three Variable System of Equations

In math we previouly learned about solving systems of equations in thee variables. To show an example of this concept I will be solving a word problem on this subject.

The problem:
You have $25 to spend on picking 21 pounds of three different types of apples in an orchard. The Empire apples cost $1.40 per pound, the Red Delicious apples cost $1.10 per pound, and the Golden Delicious apples cost $1.30 per pound. You want twice as many Red delicious apples as the other two combined.

Part A: Write a system of equations to represent the given information.
x= #of Empire apples
y= #of Red Delicious apples
z= # of Golden Delicious apples

Equation 1: x+y+z=21
Equation 2: 1.40x+1.10y+1.30z=25
Equation 3: y=2(x+z) ----> -2x+y-2z=0

Part B: How many pounds of each type of apple should you buy?

x+y+z=21
(-2x+y-2z=0) -1 --> 2x-y+2z=0
-----------------
3x+3z=21
x=-z+7

x+y+z=21
-z+7+y+z=21
7+y=21
y=14

1.4x+1.1y+1.3z=25
1.4(-z+7)+1.1(14)+1.3z=25
-1.4z+9.8+15.4+1.30z=25
-.10z+25.2=25
-.10z=-.20
z=2

x+y+z=21
x+14+2=21
x+16=21
x=5

(5,14,2)
5 pounds of Empire Apples
14 pounds of Red Delicious Apples
2 pounds of Golden Delicious Apples