Question

Question #f11c8

Answer 1

The answer is d) `"4.41 g"`.

Explanation:

The trick here is to realize that the mass of added sugar will increase the total mass of sugar and the total mass of the solution.

Your initial solution is `10%` sugar by mass, which means that every `"100 g"` of this solution contain `"10 g"` of sugar. You can thus say that the initial solution contains

`75 color(red)(cancel(color(black)("g solution"))) * "10 g sugar"/(100color(red)(cancel(color(black)("g solution")))) = "7.5 g sugar"`

Let's say that you are going to add `x` `"g"` of sugar to this solution to get its percent concentration to `15%`. At this point, the solution will contain `"15 g"` of sugar for every `"100 g"` of solution.

The mass of the solution will be

`"75 g" + x color(white)(.)"g" = (75 + x)` `"g"`

This means that the second solution will contain

`(75 + x) color(red)(cancel(color(black)("g solution"))) * "15 g sugar"/(100color(red)(cancel(color(black)("g solution")))) = 0.15 * (75 +x)` `"g sugar"`

But you already know that the mass of sugar will also be equal to

`"7.5 g" + xcolor(white)(.)"g" = (7.5 + x)` `"g"`

You can thus say that

`0.15 * (75 + x) color(red)(cancel(color(black)("g"))) = (7.5 + x)color(red)(cancel(color(black)("g")))`

Solve this for `x` to get

`11.25 + 0.15x = 7.5 + x`

`3.25 = 0.85x implies x = 3.25/0.85 = 4.41`

Therefore, you can say that if you add `"4.41 g"` of sugar to `"75 g"` of `10%` by mass sugar solution, you will get `"79.41 g"` of `15%` by mass sugar solution.