Question

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?
○ 0.02
○ 0.04
○ 0.05

Explanation:

Step1: Set up the equation for total ethanol

The amount of ethanol in the \(x\%\) solution is \(20\times\frac{x}{100}\) (since \(x\%\) is \(\frac{x}{100}\) as a decimal), in the \(12\%\) solution is \(60\times0.12 = 7.2\), and in the mixture is \(80\times0.10=8\). So the equation is \(20\times\frac{x}{100}+7.2 = 8\).

Step2: Simplify the equation

First, simplify \(20\times\frac{x}{100}\) to \(\frac{20x}{100}=\frac{x}{5}\). So the equation becomes \(\frac{x}{5}+7.2 = 8\).

Step3: Solve for x

Subtract 7.2 from both sides: \(\frac{x}{5}=8 - 7.2=0.8\). Then multiply both sides by 5: \(x = 0.8\times5 = 4\). But since we need the decimal form (as the options are in decimals), \(x\% = 4\%\) which is \(0.04\) as a decimal.

Answer:

0.04