Question 1192851
<br>
The traditional formal algebraic approach is to write and solve an equation that says (very logically!) that the sum of the amounts of alcohol in the two ingredients is equal to the amount of alcohol in the mixture.<br>
In this problem, you are starting with 8 ounces of which 20% is alcohol, adding x ounces of which 15% is alcohol, to end up with (8+x) ounces, of which 19% is alcohol.  So the equation would be<br>
{{{.20(8)+.15(x)=.19(8+x)}}}<br>
This is solved using basic algebra....<br>
{{{1.6+.15x=1.52+.19x}}}
{{{0.08=.04x}}}
{{{x=0.08/.04=2}}}<br>
ANSWER: 2 ounces of 15% alcohol<br>
CHECK:
.20(8)+.15(2)=1.6+.3=1.9
.19(10)=1.9<br>
If a formal algebraic solution is not required, you can try either of these other two methods, closely related to each other but very different from the formal algebraic method.<br>
(1) The target percentage 19 is "4 times as close to 20% as it is to 15%", so the mixture must use 4 times as much of the 20% alcohol as it does 15% alcohol.  Since the mixture uses 8 ounces of the 20% alcohol, the amount of 15% alcohol must be 1/4 of 8 ounces, which is 2 ounces.<br>
OR....<br>
(2) The target percentage 19% is 4/5 of the way from 15% to 20%, so 4/5 of the mixture must be the 20% alcohol.  Since that 4/5 of the mixture that is 20% alcohol is 8 ounces, the 1/5 of the mixture that is the 15% alcohol must be 8/4 = 2 ounces.<br>