Using linear Systems to Solve Problems

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Homework Help Overview

The discussion revolves around a problem involving the mixing of two types of gasoline to create a middle octane gasoline. The prices of premium and regular gasoline are provided, along with the total volume of the mixture to be produced. Participants are attempting to establish the correct equations to solve for the volumes of each type of gasoline used in the mixture.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to formulate a second equation based on the pricing of the gasoline mixture but expresses confusion about its correctness. Other participants suggest substituting variables and solving for the percentage of premium gasoline, while questioning the algebraic steps taken.

Discussion Status

Participants are actively engaging in the problem, with some offering algebraic manipulations and suggestions for substitution. There is a recognition of potential errors in the original poster's calculations, but no consensus has been reached on the correct approach or solution.

Contextual Notes

There is an indication of confusion regarding the setup of the equations, particularly the interpretation of the second equation related to the pricing of the gasoline mixture. Participants are working within the constraints of the problem as presented, without additional information.

msimard8
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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):

[tex]78.9 x + 71.9 (1-x) = 73.9[/tex]

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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