<p>i have a couple of questions, so if any of the CC'ers know why the answer is, i'd really appreciate the explanations. thanks guys :)</p>
<p>pg 721 number 18</p>
<h2>The average of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the socres of both classes are combined, the average score is 86. What is the value of p/n?</h2>
<p>pg 738 number 20</p>
<h2>this problem comes with a diagram, and since i cant really post the diagram, it'd be great if you guys can just explain it.</h2>
<p>pg 744 number 4</p>
<h2>The scenic route from Mia's home to her office is 5 kilometers longer than the direct route. When she goes by the scenic route and retursn by the direct route, the round trip is 35 kilometers. How many kilometers is the direct route?</h2>
<p>pg 747 number 16</p>
<h2>In rectagle ABCD, point E is the midpoint of BC. If the area of quadrilateral ABED is 2/3, what is the area of rectangle ABCD?</h2>
<p>i'm taking the SATs for the first time on the 14th, which is next week.. AH! so any help would be great thanks!</p>
<p>4.0 had a great explantion for # 16 - I just figured out (deduced :)) that triangle DEC = 1/4 of quadriteral ABED which = 2/3 so the entire thing would equal (2/3)/(3/4)...</p>
<p>The problem states that there are two classes one with p students and one with n students.</p>
<p>In the class with p students the average was 70, although not every student necessarily got a 70 if you were to assume that every student got a 70 the numbers would all come out the same. So you assume that p students got a 70 and by the same reasoning you can assume that n students got a 92.</p>
<p>So now you can set up the equation based on the definition of an arithmetic mean.</p>
<p>So you would add 70 p times and 92 n times and then divide by the total which is equal to p + n.</p>
<p>Also:</p>
<p>A much quicker method that may be more difficult to understand.</p>
<p>since the total average is closer to 70 than 92 that means that the 92 had a greater impact on the total average meaning that there must be more students in the class with an average of 92. This means that n is larger than p.</p>
<p>Now notice that 92 is 6 away from 86 while 70 is 16 away from 86. This means that the ratio between p and n is 6:16 or 3:8.</p>
<p>Since we know that n is larger than p, n has to be the 8, and p is the 3. (This doesn't mean that p=3 and n=8 but we can make that assumption and get the same answer since the fraction would need to be reduced anyway).</p>
<p>So p/n = 3/8 or .375</p>
<p>*I explained the second method as well as I could if you don't understand it just ignore it and use the first method. I only included it because it is how I would personally solve the problem and it is much quicker.</p>
<p>PS. I am also taking the SAT's for the first time on March 14, Good Luck</p>