You've poured some 8% (by mass) alcohol solution and some 12% alcohol solution into a large glass mixing container. Now you have 760 grams of 10% alcohol solution. How many grams of 8% solution and how many grams of 12% solution did you pour into the mixing container?

Step-by-step explanation:

you mixed an 8% and a 12% solution together.

so, you get (8%×mass1 + 12%×mass2)/((mass1 + mass2)/2) as resulting % of the combined solution.

since the result is 10%, which is precisely the arithmetic middle

(8 + 12)/2

we see that mass1 = mass2.

in other words : the same quantity (mass) of the 8% solution and the 12% solution was mixed together.

so, 760g = 2×mass

=>

mass = 380g

380g of the 8% solution and 380g of the 12% solution were mixed together.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80