A 45.0g aqueous solution is made using 10.0g of ethanol. What percentage of the solution is ethanol?

Your aim here is to find the mass of ethanol present in#"100 g"# of solution, which is essentially what you're referring to when talking about the solution's percent concentration by mass, #"% m/m"#.

You know that the total mass of the solution is equal to #"45.0 g"#. This mass includes the mass of water, your solvent, and the mass of ethanol, your solute.

Now, this solution has a uniform composition, meaning that the solvent and the solute are evenly mixed. This implies that you can use this given composition to figure out how many grams of ethanol would be present in #"100 g"# of solution

#100 color(red)(cancel(color(black)("g solution"))) * overbrace("10.0 g ethanol"/(45.0color(red)(cancel(color(black)("g solution")))))^(color(purple)("known composition")) = "22.2 g ethanol"#

Because #"100 g"# of solution contain #"22.2 g"# of ethanol, you can say that the solution's percent concentration by mass is equal to

#color(green)(bar(ul(|color(white)(a/a)color(black)("% m/m" = "mass of ethanol in 100 g solution" = 22.2%)color(white)(a/a)|)))#

The answer is rounded to three sig figs.