<li><p>the price of ground coffee beans is d dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d, what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee?</p></li>
<li><p>In rectangle ABCD, point E is the midpoint of side BC. If the area of quadrilateral ABED is 2/3, what is the area of rectuangle ABCD?</p></li>
<li><p>10W car is half as fast as 5W car
15W car is half as fast as 10W car
20W car is half as fast as 15W car. A car with 5W is how many times as fast as car engine oil with a rating of 20W?</p></li>
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<p>Please explain to me the easiest trick to diong these. I dont understand how to do them even though I know the anwers from the book. THanks</p>
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<li> the price of one ounce = d/8, 1 cup= 1ounce/c</li>
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<p>so
(d/8)/c= price of 1 cup =d/8c is the price of one cup</p>
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<li><p>Label BE X, and AB Y. The way I would do it is break the whole rectangle into 4 equal right rectangels of height Y and base X.
so ABED is made by 3 right triangles 3x=2/3, so the are of one triangle is 2/6...now the ABCD = 4( 2/6) = 8/6</p></li>
<li><p>Label 5W as x
so 10W= 1/2(x)
15W= 1/2(10W)= 1/2(1/2(x))
20W= 1/2(15W)= 1/2(1/2(1/2(x)))
20W=1/8x so 5w is 8 times as fast as a 20W</p></li>
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<p>I'd just like to add something that's been useful to me in solving problems like #1.</p>
<p>The math portion often has a question with many variables that attempt to confuse the test taker.</p>
<p>It's worth mentioning that a lot of these questions can be solved through a proportion.</p>
<p>Here we can use the proportion
price/cup = constant</p>
<p>So we plug in our values in the proportion price/cup = d/8c = x/1 (note that x is the variable I used to find the cost of 1 cup). So x is simply d/8c, our answer.</p>
<p>on problems like #3, megaman's method definitely works, but i find it easier just to plug in a number for 5W, double it for 10W, double it again for 15W, and double that result for 20W. Then divide the answer you got for 20W by the number of 5W.</p>
<p>for example:
5W...2 (just a random # i selected)
10W...4
15W...8
20W...16 </p>
<p>Use what is called "dimensional" or "unit" ananysis in chemistry. First, you ignore all of the context and pick out (i.e., underline) the math phrases:</p>
<p>d dollars for 8 ounces</p>
<p>each ounce makes c cups</p>
<p>what is the dollar cost?</p>
<p>one cup</p>
<p>Second, write the math phrases as fractions (note: I would write them with the numerator over the denominator, but I am limited in this post by the word processor):</p>
<p>(a) $d/8 oz</p>
<p>(b) 1 oz/c cups</p>
<p>(c) $___ (this is the question)</p>
<p>(d) 1 cup/1 (note: I put a 1 in the denominator to create a fraction)</p>
<p>Third, multiply the fractions (a), (b) and (d), so that all the units cancel out except the $ in the numerator. (Tip: start with (a) because it contains the unit of the answer.)</p>
<p>($d/8 oz)(1 oz/c cups)(1cup/1) = $____</p>
<p>Finally, after you have canceled out all of the units, except for the $, multiply what's left in the numerator and denominator separately to get your final answer. d/8c</p>
<p>I would use this technique whenever the problem involves fractions with multiple units. Ignore the context and ignore the phrase like "in terms of c and d". They are not important and will only slow you down.</p>
<p>^Why did you revive a 2 year old thread?!?!?!?!?!
Oh and for the brewed coffee question, the logical method is
the Total cost/Total Cups = cost per cup right?</p>
<p>Then the total cost is already given, which is D and since each ounce makes c cups, then 8c = the total amount of cost, making the answer d/8c.</p>
<p>Then you don't really need to do dimensional analysis or does this way make no sense...</p>
<p>Just draw a picture or something. You will see that ABED is 3/4 of the total rectangle. Just do some simple math after that. If the total is x then:</p>