Question

solving mixture problems
maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. the table shows the amount of each solution.
ethanol mixture

	gallons	ethanol concentration	total
12% ethanol	60	0.12	7.2
mixture	80	0.10

what is the value of $x$, the concentration of the unknown ethanol solution?
options: 0.02, 0.04, 0.05, 0.08

Explanation:

Step1: Recall mixture formula

The total ethanol in the mixture is the sum of ethanol from each solution. So, \(20x + 60\times0.12 = 80\times0.10\).

Step2: Simplify the equation

Calculate \(60\times0.12 = 7.2\) and \(80\times0.10 = 8\). The equation becomes \(20x + 7.2 = 8\).

Step3: Solve for x

Subtract 7.2 from both sides: \(20x = 8 - 7.2 = 0.8\). Then divide by 20: \(x=\frac{0.8}{20}=0.04\).

Answer:

0.04