Question f11c8

Apr 13, 2017

The answer is d) $\text{4.41 g}$.

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 $\text{100 g}$ of this solution contain $\text{10 g}$ 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 $x$ $\text{g}$ of sugar to this solution to get its percent concentration to 15%. At this point, the solution will contain $\text{15 g}$ of sugar for every $\text{100 g}$ of solution.

The mass of the solution will be

$\text{75 g" + x color(white)(.)"g} = \left(75 + x\right)$ $\text{g}$

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) $\text{g sugar}$

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

$\text{7.5 g" + xcolor(white)(.)"g} = \left(7.5 + x\right)$ $\text{g}$

You can thus say that

$0.15 \cdot \left(75 + x\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g"))) = (7.5 + x)color(red)(cancel(color(black)("g}}}}$

Solve this for $x$ to get

$11.25 + 0.15 x = 7.5 + x$

$3.25 = 0.85 x \implies x = \frac{3.25}{0.85} = 4.41$

Therefore, you can say that if you add $\text{4.41 g}$ of sugar to $\text{75 g}$ of 10% by mass sugar solution, you will get $\text{79.41 g}$ of 15%# by mass sugar solution.