This is a system of equations question in disguise. As with every system of equations question, it's best to call/ define some variables.
I'm going to say that:
A = the COST of a gallon of anti-freeze
W = the COST of a gallon of water
Note that I defined the variables not as the amount of fluid, but the cost of each fluid.
From the information given we can write two equations. The first being:
A = 12.99
This is stating that the cost of a gallon of anti freeze is 12.99.
The second equation is a bit more tricky to put together. You essentially have half a gallon of water and half a gallon of anti-freeze. You know that this totals $10.99. So you can state that:
A*1/2 + W*1/2 = 10.99
This is saying that the cost of half a gallon of antifreeze (A*1/2) PLUS the cost of half a gallon of water (W*1/2) EQUALS 10.99.
From the first equation we can substitute a real value in for A.
12.99*1/2 + W*1/2 = 10.99
This is now 1 equation, 1 unknown, and is entirely solvable.
6.495 + W/2 = 10.99
W/2 = 4.495
W = 8.99
From the definition of our variables above, this equation is saying the cost of the gallon of water is $8.99.
Tap water from your sink is a less than a penny per gallon. I think in California it's about 1/5 of a cent, meaning 5 gallons of water will cost you a penny. Best just to buy the pure anti-freeze and dilute it at home.
Hope this helps.