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Math Help - Mixture Application

  1. #1
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    Mixture Application

    Granny needs 3 gallons of 15% vinegar for her pickles. Bud went to the store and bought 2 gallons of 50% vinegar. Granny asks: How much pure spring water must I mix with some of that 50% stuff to get my cantaner filled with 3 gallons of 15% solution?

    [first mixture] + [second mixture] = [total mixture]

    [3(0.15)] + [x(0.50)] = [(x + 3)(0.15)]

    Is this the correct equation and set up?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magentarita View Post
    Granny needs 3 gallons of 15% vinegar for her pickles. Bud went to the store and bought 2 gallons of 50% vinegar. Granny asks: How much pure spring water must I mix with some of that 50% stuff to get my cantaner filled with 3 gallons of 15% solution?

    [first mixture] + [second mixture] = [total mixture]

    [3(0.15)] + [x(0.50)] = [(x + 3)(0.15)]

    Is this the correct equation and set up?
    nope, that's not the set up.

    first of all, we want the final mixture to be 3 gallons. as you have it, we would have more than that. secondly, we are mixing pure water with vinegar solution. so one mixture has no vinegar in it.

    also, a technicality here. you have an expression with x and never said what x was. that is bad practice! a good mathematician always identifies his/her variables and try to keep the ambiguity to a minimum.

    so start this way: let x be the amount (in gallons) of spring water we want to add to make up our 3 gallon mixture. and let y be the amount (in gallons) of the 50% vinegar solution we add to the said mixture.

    our first equation is x + y = 3. since we want both gallon amounts to add up to 3 gallons.

    now, what is the second equation? remember, we want to get 0.45 gallons (15% of 3 gallons) in the final mixture.
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  3. #3
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    Thanks but.....

    Quote Originally Posted by Jhevon View Post
    nope, that's not the set up.

    first of all, we want the final mixture to be 3 gallons. as you have it, we would have more than that. secondly, we are mixing pure water with vinegar solution. so one mixture has no vinegar in it.

    also, a technicality here. you have an expression with x and never said what x was. that is bad practice! a good mathematician always identifies his/her variables and try to keep the ambiguity to a minimum.

    so start this way: let x be the amount (in gallons) of spring water we want to add to make up our 3 gallon mixture. and let y be the amount (in gallons) of the 50% vinegar solution we add to the said mixture.

    our first equation is x + y = 3. since we want both gallon amounts to add up to 3 gallons.

    now, what is the second equation? remember, we want to get 0.45 gallons (15% of 3 gallons) in the final mixture.
    Thank you but Soroban already solved this for me.
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