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

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