Help with a mixture problem?

How many gallons of a 30% acid solution must be added to how many gallons of a 70% acid solution to make 50 gallons of a 40% acid solution?

I have no idea how to solve this.  Most helpful explanation will be awarded best answer.

4 Answers

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  • 1 month ago

    Start by defining a variable.

    Let x be the amount of 30% acid solution (in gallons)

    The rest of the mixture will add up to 50 gallons, so that means you have 50 - x of the second solution.

    Let 50 - x represent the amount of 70% acid solution (in gallons).

    Now write an expression for the amount of acid that results from the mixture.

    0.30x + 0.70(50 - x)

    That must be equal to 0.40 of a 50 gallon mix.

    0.30x + 0.70(50 - x) = 0.40 * 50

    Now we can expand and simplify:

    0.3x + 35 - 0.7x = 20

    -0.4x + 35 = 20

    -0.4x = -15

    x = -15 / -0.4

    x = 15 / (2/5)

    x = 15 * 5/2

    x = 75/2

    x = 37.5 gallons <-- amount of 30% acid solution

    And the remaining amount (50 - x) would be the other solution

    50 - x = 12.5 gallons <-- amount of 70% acid solution

  • Ian H
    Lv 7
    1 month ago

    0.3n + 0.7(50 – n) = 0.4*50

    35 - 20 = 0.4n

    n = (5/2)*15 = 37.5 gallons (of the 30%)

  • 1 month ago

    50 gallons of a 40% acid solution means 20 gal of acid and 30 gal of water

    30% has 0.3 gal per gal, call quan. of solution x

    70% has 0.7 gal per gal, call quan. of solution y

    0.3x + 0.7y = 20

    x + y = 50

    multiply by 10 and –3 and add

    3x + 7y = 200

    –3x – 3y = –150

    4y = 50

    y = 12.5 gal

    x = 50–12.5 = 37.5 gal

    check

    37.5 gal of 30% = 11.25 gal acid

    12.5 gal of 70% =   8.75 gal acid

    total                       20 gal acid

  • 1 month ago

    50 gallons of a 40% solution is 50(.4) = 20 gallons of pure acid.

    Let x be the gallons of 30% solution to be added.

    Let y be the gallons of 70% solution to be added.

    x + y = 50

    .3x + .7y = 20

    x = 75/2 = 37.5 gallons

    y = 25/2 = 12.5 gallons

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