Let's define the following variables.
x = amount of $8 sparkling water
y = amount of $3 sparkling water
z = amount of $4.50 sparkling water
If we want to create 200 gals of sparkling water then we can form the equation below:
[tex]x+y+z=200gal[/tex]
"She must use twice as much of the $4.50 water as the $3.00 water" means the amount of z must be twice to equate to y.
[tex]z=2y[/tex]
Using the value of y, we can rewrite equation 1 as:
[tex]\begin{gathered} x+y+2y=200 \\ x+3y=200 \end{gathered}[/tex]
Then, applying the cost per gallon in each type of sparkling water, we have another equation:
[tex]\begin{gathered} 8x+3y+4.50z=200(5) \\ 8x+3y+4.50z=1000 \\ 8x+3y+4.50(2y)=1,000 \\ 8x+3y+9y=1000 \\ 8x+12y=1000 \end{gathered}[/tex]
To summarize, we have:
Equation 1: x + 3y = 200
Equation 2: 8x + 12y = 1000
Graphing these two equations, we get:
The intersection of the two equations is at (50, 50)c
Therefore, the value of x = 50 gallons and the value of y = 50 gallons.
Now, since z = 2y, ten xz = 2(50) = 100 gallons. z = 100 gallons
In conclusion,
50 gallons of $8.00 sparkling water
50 gallons of $3.00 sparkling water
100 gallons of $4.50 sparkling water
