Question 1203535
<br>
The standard algebraic solution looks something like this:<br>
100 ml of 22% alcohol, plus x ml of 100% alcohol, yields (100+x) ml of 70% alcohol.<br>
{{{.22(100)+1.00(x)=.70(100+x)}}}
{{{22+x=70+.7x}}}
{{{.3x=48}}}
{{{x=48/.3=160}}}<br>
ANSWER: 160 ml<br>
Here is an alternative, informal method which often makes reaching the answer easier.<br>
Picture a number line showing the three percentages -- 22, 70, and 100.  Calculate that 70 is 48/78 of the way from 22 to 100 (22 to 70 is a difference of 48; 22 to 100 is a difference of 78).<br>
That fraction 48/78 means the two ingredients must be mixed in the ratio 48:(78-48) = 48:30 = 8:5. Since 70% is closer to 100% than to 22%, the larger portion must be the 100% alcohol.  Then we have the proportion<br>
{{{8:5=x:100}}}
{{{5x=800}}}
{{{x=160}}}<br>
And again of course the answer is 160 ml.<br>