Question #f11c8

1 Answer
Apr 13, 2017

Answer:

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.