# Using linear Systems to Solve Problems

1. Sep 26, 2006

### msimard8

Simple Question, just need help establising second formula

Premium gasoline sells for 78.9/L. Regular gas sells of 71.9/L. To boost sales, a middle octane gasoline is formed by mixing premuium and regular. If 1000 L of this middle octane gas is prodcued ,and is sold at 73.9/L, then how much of each type of gasoline can you assume was used in the mixture. (units are in cents)

i got my first formula

x + y = 1000

its the second formula that confuses me

this is my incorrect one
78.9 x + 71.9 y = 73.9 (1000)

help

2. Sep 26, 2006

### Staff: Mentor

Looks okay to me. The next step is to realize that y = 1000 - x, and substitute that into the 2nd equation.

3. Sep 26, 2006

### msimard8

is that 2nd equation is right

the answer is 600 L of premium, and 400 L or regualar

that equation doenst get that

4. Sep 26, 2006

### Staff: Mentor

I think it's just your algebra. Try solving this form to find the percentage of premium (your x variable):

$$78.9 x + 71.9 (1-x) = 73.9$$

Distribute x and solve. No calculator required.

EDIT -- I recast your x into the percentage. In your initial equation, it is the percentage multiplied by 1000L. Sorry for any confusion.

Last edited: Sep 26, 2006
5. Sep 26, 2006

### msimard8

got x=2/7

which is obviously not 600.

still something must be wrong

6. Sep 26, 2006

### Staff: Mentor

Yeah, see my edit above. That should clear it up.