full strength anti freeze is 12.99 a gallon. they also sell a 50/50 pre-mix which is diluted 50% with water for 10.99 a gallon.

Question

Full question: full strength anti freeze is 12.99 a gallon. they also sell a 50/50 pre-mix which is diluted 50% with water for 10.99 a gallon. how much are you paying per gallon for water if you buy premix 

 

Any Helo would be greatly appreciated my teacher is lacking showing us how to get the answer and for someone who struggles with math I have no idea what numbers to plug in or what formulas to use... 

Answer 1

Hi LEX.

 

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.