How much of a 50% Alcohol solution should we mix with 10 gallons of 35% solution to get 40% solution

Question

How much of a 50% Alcohol solution should we mix with 10 gallons of 35% solution to get 40% solution

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Allison 2 weeks 2021-11-23T21:10:59+00:00 1 Answer 0 views 0

Answers ( )

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    2021-11-23T21:12:28+00:00

    5 gallons of 50 % alcohol solution is used

    Solution:

    Let “x” is the gallons of 50 % alcohol solution

    Then, 10 gallons is 35 % solution

    The, 10 + x is the gallons of 40 % solution

    Then, according to question,

    “x” gallons of 50 % solution is mixed with 10 gallons of 35 % solution to get 10 + x gallons of 40 % solution

    Therefore,

    50 \% \times x + 35 \% \times 10 = 40 \% \times (10+x)\\\\\frac{50}{100} \times x + \frac{35}{100} \times 10 = \frac{40}{100} \times 10+x\\\\0.5x + 3.5 = 0.4(10+x)\\\\0.5x + 3.5=4+0.4x\\\\0.5x-0.4x = 4-3.5\\\\0.1x = 0.5\\\\Divide\ both\ sides\ by\ 0.1\\\\x = 5

    Thus 5 gallons of 50 % alcohol solution is used

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45:7+7-4:2-5:5*4+35:2 =? ( )