<p>Just wondering if anyone can explain to me how to solve these problems. </p>
<p>If (v/v+1)(1/v)(v/v-1)=7/w for positive integers v and w, what is the value of w?
A. 1
B. 7
C. 48
D. 49
E. 50</p>
<p>The answer is C, but how would you go about solving this problem?</p>
<p>A banquet hall can only be reserved for groups numbering between 40 and 60 people. Which of the following inequalities can be used to determine whether or not the banquet hall can be reserved for a group of p people?
A. |p-20| < 50
B. |p-30| < 40
C. |p-40| < 20
D. |p-50| < 10
E. |p-55| < 5</p>
<p>Answer is D.</p>
<p>The figure (I tried typing it out, but was messed up) above represents a single piece of cardboard. It can be folded along the dotted lines to form a rectangular solid with square ends, a longest side of 12 inches, and a volume of 300 cubic inches. If the piece was cut from a square sheet of cardboard, what was the minimum area of the square sheet, in square inches?
A. 220
B. 300
C. 400
D. 440
E. 484</p>
<p>Answer’s E.</p>
<p>I can help with #2.</p>
<p>All of the equations feature the same form: |x|< y. Let’s look at D:</p>
<p>|p-50| < 10. Recall that the definition of absolute value states that if you have the form |x|< y, this simplifies to -y < x < y. </p>
<p>So, applying that definition, we get:
-10 < p-50 < 10 - Add 50 to each part of the inequality to get:
40 < p < 60. This is what we are looking for. p is a number of people between 40 and 60, exactly what the problem was asking for.</p>
<p>Because someone did 2 and I’m lazy, I’ll do only 1.</p>
<p>How I would do it is choose two numbers for v and solve for w. If they both are the same then, that’s the answer. (I love the plug it in way)</p>
<p>^ I answered the question using the plug-in method as well, but is there a more mathematical approach to the question?</p>
<p>Also, the figure in the third question looks like an upside down T. It has 3 rectangles that are 12 in. across as the | part of the T. The __ part of the T is a square rectangle square.</p>
<p>since you wanted a more mathematical approach to #1, here it is</p>
<p>after clearing out the mess on the left side, you are left with</p>
<p>[ v / ((v^2)-1) ] = ( 7 / w )</p>
<p>there’s a rule which states that when (a/b) = (c/d), then a = c and b = d</p>
<p>applying that to our example, we get v=7 and (v^2)-1 = w</p>
<p>w = 48 (C)</p>
<p>Thanks guys for the help.</p>
<p>^ Can’t believe I didn’t see that. I got it down to a/b = c/d but didn’t see that at all.</p>
<p>Anyone know how to solve the third problem?</p>
<p>Probably, but I can’t tell if I’m visualizing the problem right.</p>
<p>Would I be able to draw it on paint and attach a link to it from imageshack or is that not possible on this forum?</p>
<p>That would be great.</p>
<p>Excellent. I figured it out easily. The dimensions of your square piece of cardboard are 22x22 = 484 area. Let me explain.</p>
<p>Since a rectangular solid with square ends having a volume of 300 is formed, you need the dimensions of this shape. We know that volume = length x width x height. We know one length and the fact that the other two are equal (sides of the square). I divided 300/12 to get 25. This means that the square ends have a length of 5. 5 x 5 x 12 = 300. </p>
<p>Now, I used the fact that one side of the square of cardboard is made up of the 12 inch strip plus two 5 inch strips, judging from the bottom part of the diagram you drew. This means that the each side of the square has length 22, giving an area of 484.</p>
<p>Understand?</p>
<p>Ah, all makes sense now. Thanks so much!</p>
<p>No problem! Helping other people out is good practice for me as well. :p</p>
![http://img101.imageshack.us/i/satmath.jpg/]Imageshack](http://img101.imageshack.us/i/satmath.jpg/%5DImageshack){kind=link}
