<p>Here's today's SAT Question of the Day I found confusing. Does anyone have a quick, efficient way of doing it, or at least a helpful explanation? Thanks.</p>
<p>In an 8-gram solution of water and alcohol, the ratio by mass of water to alcohol is 3 to 1. If 12 grams of a solution consisting of 2 grams water for each gram of alcohol is added to the 8-gram solution, what fraction by mass of the new solution is alcohol?</p>
<p>Ans: 3/10</p>
<p>First change the ratios to fractions. 3 water to 1 alcohol = of every 4 grams, 3 are water, 1 is alcohol. Of the 8 grams of the original solution 2 are alcohol (1 out of every 4). Of the 12 grams of the second solution 4 are alcohol (1 out of every 3). Add them together and you get 6 grams of alcohol (2+4) out of 20 grams of solution (8+12) and simplify to get 3/10.</p>
<p>Ok. Thanks so much. The way the question is worded is pretty nasty. I tend to have trouble converting ratios (3 TO 1) to fractions (1/4 and 3/4).</p>
<p>Just remember ratios are not quite the same as fractions – if the ratio of boys to girls is 3:4, the corresponding fraction of boys is not 3/4 but instead 3/7.</p>
<p>Thanks. That helps a lot!</p>