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Math Help - Algebra Word Problems

  1. #1
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    Question Algebra Word Problems

    I have 2 word problems in which I need to set up the equation and arrive at an answer. I am not exactly asking for an answer to these problems, I just need help in setting the labels and equations up. For question one I have most of the information, but not for question two. The areas typed in red are the areas that I need help with. THANK YOU SOOOO MUCH!!!


    1) A chemist needs 140 mL of a 32% solution but has only 22% and 50% solutions available. Find how many mL of each that should be mixed to get the desired solution.
    *(Verbal Model): #of mL of 22% solution + # of mL of 50% solution=140mL of 32% solution
    *(Labels): #of mL of 22% solution=x, #of mL of 50% solution=140-x, amount of 22% solution=0.22x, amount of 50% solution= .50(???), amount of 32% solution= .32(???)
    *(Equation): .22x + .50(???) = .32(???)


    2) Two pumps can fill a water tank in 45 minutes when working together. Alone the second pump takes 3 times longer than the first to fill up the tank. How long does it take the first pump alone to fill the tank?
    *(Verbal Model):
    *(Labels):
    *(Equation):
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  2. #2
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    Quote Originally Posted by kanej316 View Post
    ...


    1) A chemist needs 140 mL of a 32% solution but has only 22% and 50% solutions available. Find how many mL of each that should be mixed to get the desired solution.
    *(Verbal Model): #of mL of 22% solution + # of mL of 50% solution=140mL of 32% solution
    *(Labels): #of mL of 22% solution=x, #of mL of 50% solution=140-x, amount of 22% solution=0.22x, amount of 50% solution= .50(???), amount of 32% solution= .32(???)
    *(Equation): .22x + .50(???) = .32(???)


    ...
    You only have to do one step and use all the terms you've found by yourself:

    0.22 \cdot x + 0.50 \cdot (140-x) = 0.32 \cdot 140

    Expand the bracket and solve for x. (For confirmation only: x = 90)
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  3. #3
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    Quote Originally Posted by kanej316 View Post
    ...
    2) Two pumps can fill a water tank in 45 minutes when working together. Alone the second pump takes 3 times longer than the first to fill up the tank. How long does it take the first pump alone to fill the tank?
    *(Verbal Model):
    *(Labels):
    *(Equation):
    Let T denote the volume of the tank and x the number of minutes, it takes the first pump to fill the tank.

    Then the second pump will need 3x minutes to fill the tank.

    \dfrac Tx is the amount of water which comes from the first pump in one minute;

    \dfrac T{3x} is the amount of water which comes from the second pump in one minute.

    Together they are working during 45 minutes and then the tank is filled:

    \left(\dfrac Tx + \dfrac T{3x}  \right) \cdot 45\ min = T

    Expand the bracket and solve for x. (For confirmation only: x = 60)
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