Let's call x, y, and z the $10, $1, and $4.50 water respectively.

Because the total is 300 gallons.
"She must use twice as much of the $4.50 water as the $1.00 water" we express it like this

We combine equations

We know that we have to mix all three grades of water for $6.

We combine the second equation with the last one

Now, we combine the last question with x+3y = 300 to make a system

We multiply the second equation by -1, then we combine the equations to solve for y

This means she should use 60 gallons of the $1 water.
Then,

She should use 120 gallons of the $10 water.
At last,

She should use 120 gallons of $4.50 water.