Using linear Systems to Solve Problems

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The discussion focuses on solving a problem involving the mixing of premium and regular gasoline to create a middle octane fuel. The first equation established is x + y = 1000, representing the total volume of the mixture. The confusion arises with the second equation, initially set incorrectly, but it is clarified that substituting y with 1000 - x leads to the correct formulation. The solution ultimately reveals that 600 liters of premium and 400 liters of regular gasoline are used in the mixture. The participants emphasize the importance of proper algebraic manipulation to arrive at the correct answer.
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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
 
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Looks okay to me. The next step is to realize that y = 1000 - x, and substitute that into the 2nd equation.
 
is that 2nd equation is right

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

that equation doenst get that
 
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:
got x=2/7

which is obviously not 600.

still something must be wrong
 
msimard8 said:
got x=2/7

which is obviously not 600.

still something must be wrong
Yeah, see my edit above. That should clear it up.
 

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