The chemistry class was making 300 gallons of 30% isopropyl alcohol. They mixed 12% with 42%. How much of each did they use?

Question

The chemistry class was making 300 gallons of 30% isopropyl alcohol. They mixed 12% with 42%. How much of each did they use?

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Jasmine 2 weeks 2021-09-15T01:41:20+00:00 1 Answer 0

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    2021-09-15T01:42:21+00:00

    Answer:

    The chemistry class mixed 120 gallons of 12% isopropyl alcohol and 180 gallons of 42% isopropyl alcohol.

    Step-by-step explanation:

    1. Let’s review the information given to us to answer the question correctly:

    Amount of isopropyl alcohol made by the chemistry class = 300 of 30%

    Amount of 12% isopropyl alcohol mixed by the chemistry class = x

    Amount of 42% isopropyl alcohol mixed by the chemistry class = 300 – x

    2. How much of each did they use?

    Let’s write our equation to solve for x, this way:

    30% = 0.3, 12% = 0.12, 42% = 0.42

    0.12x + 0.42 (300 – x) = 0.3 * 300

    0.12x + 126 – 0.42x = 90

    -0.3x = 90 – 126

    -0.3x = -36

    x = -36/-0.3

    x = 120 ⇒ 300 – x = 180

    Let’s prove x = 120 is correct

    0.12x + 0.42 (300 – x) = 0.3 * 300

    0.12 * 120 + 0.42 (300 – 120) = 0.3 * 300

    14.4 + 75.6 = 90

    90 = 90

    We proved x = 120 is correct

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