How much of each type of gasoline can you assume was used in the mixture?

Question

Premium gasoline sells for 78.9 cents/litre. Regular gasoline sells for 71.9 cents/litre. To boost sales, a middle octane gasoline is formed by mixing premium and regular. If 1000 litres of this middle octane is produced, and is sold at 73.9 cents/litre, then how much of each type of gasoline can you assume was used in the mixture?

Answer 1

First, establish a variable for either premium or regular gas. If x is premium, then 1000-x should be regular, since your mixture has a total of 1000 litres (this is very important to get right, so make sure you know that complementary relationship between those variables).

 

Now you can think about the costs involved.

 

Okay, so think about balance of units here (and I like to work this in dollars rather than cents...) If you have x L of premium gas, selling at $0.789/L, the total cost of Premium should be given by 0.789x (Litres cancel out and you have a dollar unit). Similarly, Regular is given by 0.719(1000-x), and the cost of the mixture is 0.739(1000).

 

Put this all into an equation:

 

0.789x + 0.719(1000-x) = 0.739(1000)

 

Solve from there, and you'll have your x to sub back in to calculate the Litres of Premium and Regular. (that is assuming that the seller is aiming to balance selling prices fairly and not try to sneakily upcharge).