<li>If xy=2, and yz=5, and xz=10, and x>0, what is the value of xyz?
5, 10, 17, 50, 100?</li>
</ol>
<p>-I did it the long way by doing things like x=2/y, so what is the short way of doing it?</p>
<li><p>You have 10 marbles in three jars. What is the least # of marbles you can remove from one and put them in the other to make the ratio of marbles in the jars 3:2:1. Well I sort of figured it out by my own by thinking of 5, but I’ve seen a lot of these ratio problems, and want to know the algebraic way of doing it. </p></li>
<li><p>Out of 48 students in a high school, 30 study art and 25 study music and 9 do neither. How many students do both art and music?
7, 9, 11, 16, 25</p></li>
</ol>
<p>What is the algebraic way of doing these problems? I had 39 students who did the activities by subtracting 9 from 48. Then I took an answer choice, added it to two values(subtracting the answer choice from both the art and music). So say for D), 16. It would be 16+ (30-16)+(25-16), which comes out to 39. This is the long way of doing it, and I want to know what was the short way of doing it.</p>
<p>Those ways are pretty short, you have one min. per math question and usually u don't need one min on the easy questions so the way you are solving them should be fine</p>
<ol>
<li><p>That's the only way I know how to do it.</p></li>
<li><p>Again, common sense prevails over a real formula.</p></li>
<li><p>I would subtract 9 for 39, then say 30 of those 39 took art. The other 9 had to take music. 25 (total music) - 9 (only music) = 16 (art and music)</p></li>
</ol>
<ol>
<li>multiply all three together and then take the square root. (10)</li>
<li>i dont understand what its asking</li>
<li>venn diagram. (16)</li>
</ol>
<p>How would the Venn Diagram work? You have 30 in one circle, 25 in the other, and then how do you just calculate the middle using the #39?</p>
<p>As for #2, you have three jars, each with 10 marbles, so you have 30 marbles. If you remove 5 marbles from one of the jars and put them into another one of the jars, you would have 15 in one(just added to), 10 in one(unaffected), and 5 in the other(just took 5 from). So it was asking what was the least # you had to take to get the ratio 3:2:1(15:10:5). What would be an equation to do it?</p>
<p>for #2, you take x marbles from the second jar and put them in the first, so the third jar will always have 10 marbles, while the first will have 10+x and the second will have 10-x. The ratio 3:2:1 will be (10+x):10: (10-x) so (10+x)/10 = 3/2. X = 5 marbles.</p>
<p>Thanks Amber! I got lucky on the test because 5 just popped right in my mind, but it is quite a challenge to think of these convenient methods when you're trying to rush. I don't use as much algebra on the test, I usually do substitution, plugging in #s(or making them up, whether it's for this problem or the problems with many variables), etc.</p>