maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol…

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.\nethanol mixture\n| |gallons|ethanol concentration|total|\n|----|----|----|----|\n|x% ethanol|20|x||\n|12% ethanol|60|0.12|7.2|\n|mixture|80|0.10||\nwhat is the value of x, the concentration of the unknown ethanol solution?\n0.02\n0.04\n0.05

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.\nethanol mixture\n| |gallons|ethanol concentration|total|\n|----|----|----|----|\n|x% ethanol|20|x||\n|12% ethanol|60|0.12|7.2|\n|mixture|80|0.10||\nwhat is the value of x, the concentration of the unknown ethanol solution?\n0.02\n0.04\n0.05

Answer

Explanation:

Step1: Set up equation based on ethanol - amount conservation

The amount of ethanol in the first solution is $20\times\frac{x}{100}$, the amount of ethanol in the second solution is $60\times0.12 = 7.2$, and the amount of ethanol 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, rewrite $20\times\frac{x}{100}$ as $0.2x$. The equation becomes $0.2x+7.2 = 8$.

Step3: Solve for x

Subtract 7.2 from both sides of the equation: $0.2x=8 - 7.2$. So $0.2x = 0.8$. Then divide both sides by 0.2: $x=\frac{0.8}{0.2}=4$. Since $x$ is a percentage, the concentration is $4%$ or $0.04$ in decimal form.

Answer:

0.04