Question #21437

By definition, a `27%` aqueous sugar solution will contain `"27 g"` of sugar for every `"100 g"` of the solution. This means that your `"100-g"` sample contains exactly `"27 g"` of sugar.

Now, when you take `1/3"rd"` of this sample, you end up with a solution that contains

`"27 g sugar"/3 = "9 g sugar"`

in about

`"100 g solution"/3 = "33.33 g solution"`

You then add `"10 g"` of sugar to this second sample. At this point, the mass of sugar will be equal to

`"9 g + 10 g = 19 g"`

and the mass of the solution will be

`"33.33 g + 10 g = 43.33 g"`

In order to find the solution's percent concentration by mass, you need to figure out the number of grams of sugar present in exactly `"100 g"` of this solution.

To do that, use the known composition of the solution as a conversion factor

`100 color(red)(cancel(color(black)("g solution"))) * "19 g sugar"/(43.33 color(red)(cancel(color(black)("g solution")))) = "43.85 g sugar"`

You can thus say that this solution has

`color(darkgreen)(ul(color(black)("% m/m = 43.85% sugar")))`

I'll leave the answer rounded to four sig figs because it comes very close to one of the options given to you, i.e. (4) `43.84%`.