Answer:
1.8 quartz of 80% solution and
0.9 quarts of 20% solution.
Step-by-step explanation:
Given that:
Total alcohol solution to be made = 2.7 quarts of 60% solution
Alcohol concentration in first solution= 80%
Alcohol concentration in second solution = 20%
To find:
How much of each solution must Jim use?
Solution:
Let amount of first solution to be used = [tex]x[/tex] quartz
Total amount is given as = 2.7 quarts
So, amount of second solution to be used = (2.7 - [tex]x[/tex]) quartz
As per question statement, we can write the following equation:
[tex]80\%\ of\ x +20\%\ of\ (2.7-x) = 60\%\ of\ 2.7\\\Rightarrow \dfrac{80}{100} x +\dfrac{20}{100} (2.7-x) = \dfrac{60}{100}\times 2.7\\\Rightarrow 4x+2.7-x =3\times 2.7\\\Rightarrow 3x=2\times 2.7\\\Rightarrow \bold{x =1.8\ quartz}[/tex]
First solution, 80% solution to be used = 1.8 quartz
Second solution, 20% solution to be used = 2.7 - 1.8 = 0.9 quartz
