A chemist needs 80 milliliters of a 50% solution but she only has 20% and 60% solutions available. Calculate how many milliliters of each sh

Question

A chemist needs 80 milliliters of a 50% solution but she only has 20% and 60% solutions available. Calculate how many milliliters of each should be mixed to get the desired result. How many milliliters of the 20% solution should she use?

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Answers ( No )

    0
    2021-09-09T18:58:46+00:00

    Answer:

    20 mL

    Step-by-step explanation:

    Let x represent the amount of 20% solution added and y represent the amount of 60% solution added.

    Our first equation would be

    x + y = 80,

    since the amount of 20% solution and the amount of 60% solution combine to make a total of 80 milliliters.

    20% = 20/100 = 0.2; this means the 20% solution would be represented as 0.2x.

    60% = 60/100 = 0.6; this means the 60% solution would be represented as 0.6y.

    Together they make 80 milliliters of a 50% solution; this gives us the equation

    0.2x + 0.6y = 0.8(50)

    Simplifying,

    0.2x + 0.6y = 40

    This gives us the system

    \left \{ {{x+y=80} \atop {0.2x+0.6y=40}} \right.

    To solve this, we will use elimination.  Multiply the top equation by 0.2 to make the coefficients of x the same:

    \left \{ {{0.2(x+y=80)} \atop {0.2x+0.6y=40}} \right. \\\\\left \{ {{0.2x+0.2y=16} \atop {0.2x+0.6y=40}} \right.

    Subtract the bottom equation from the first:

    \left \{ {{0.2x+0.2y=16} \atop {-(0.2x+0.6y=40)}} \right. \\\\-0.4y=-24

    Divide both sides by -0.4:

    -0.4y/-0.4 = -24/-0.4

    y = 60

    There should be 60 milliliters of 60% solution.

    Substitute this into the first equation:

    x+60 = 80

    Subtract 60 from each side:

    x+60-60 = 80-60

    x = 20

    There should be 20 milliliters of the 20% solution.

    0
    2021-09-09T18:59:22+00:00

    We have 20% and 60% solutions and need 80 ml of 50%

    A) x + y = 80

    B) .20x + .60y = (80 * .5)

    Multiplying A) by -.2

    A) -.2x -.2y = -16  Then adding this to B) we get

    .4y = 24

    y = 60 ml of 60%

    x = 20 ml fo 20%

    Source: 1728.com/mixture.htm

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