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Math Help - Linear Equation type of question (fuel mixture)

  1. #1
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    Linear Equation type of question (fuel mixture)

    here is the question:

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

    Answer : 600 L premium and 400 L regular.........i got the answer from the back of the buk.....but i m not able to solve this question and get this answer

    help plz
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  2. #2
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    Quote Originally Posted by usm_67
    here is the question:

    Premium gasoline sells for 78.9cents/Liters. Regular gas sells for 71.9 cents/ litres. To boost sales, a middle octane gasoline is formed by mixing premium and regular. If 1000 L of this middle octane gas is produced, and is sold at 73.9 cents/Litres, then how much of each type of gasoline can you assume was used in the mixture?
    Answer : 600 L premium and 400 L regular.........i got the answer from the back of the buk.....but i m not able to solve this question and get this answer
    help plz
    Hello,

    I've difficulties to get the answers you mentioned above, because:
    600 * 78.9 + 400 * 71.9 = 76100. That means 1 ltr of this mddle octane gas will cost 76.1 and not - as it is said in your problem - 73.9.

    Let be x = amount of prem. gas.
    Let be y = amount of reg. gas.

    Then you get a system of linear equations:
    x + y = 1000
    78.9*x + 71.9*y=73.1*1000

    Solve this system and you'll get:

    x = 285.7 ltr
    y = 714.3 ltr.

    Greetings

    EB
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  3. #3
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    sir can u plzz solve by all steps so i can understand how u got dat anwer.
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  4. #4
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    Quote Originally Posted by usm_67
    sir can u plzz solve by all steps so i can understand how u got dat anwer.
    Hello,

    I don't know which method you are used to. I'll sho you one which is here convenient to solve this system of equations:
    (A and B are labels of an equation)

    A:\ x+y=1000
    B:\ 78.9x+71.9y=73.9 \cdot 1000

    Solve A for y: y = 1000-x (****)
    Plug in this term in B:

    B:\ 78.9x+71.9(1000-x)=73900

    B:\ 78.9x+71900-71.9x=73900. Now subtract 71900 from both sides:

    B:\ 7x=2000\ \Longrightarrow\ x=\frac{2000}{7}\approx 285.7

    Plug in this value into (****) and yo get y=1000-\frac{2000}{7}\approx 714.3

    Greetings

    EB
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