Math questions from bluebook

<p>Could you enlighten us as to the 20 second visualization technique please?</p>

<p>Sorry it took me so long to post - drawing here is a real pain!</p>

<p>After a number (any number!) of described manipulations we have two glasses with equal amount of liquid in each.</p>

<p>Let's imagine that we can separate lemonade from water in each glass and put the layers in a way we want:
water on top of lemonade in glass one,
and
lemonade on top of water in glass two.</p>

<p>We'll see this in each glass:
.____________.
|......................|
|......................|
|+++++++++++|
|......................|
|......................|
|......................|
|......................|
|......................|
|......................|
.===========.
Not drawn to scale.</p>

<p>(You should draw two such glasses next to each other).</p>

<p>The next paragrapg is optional - you might be able to see the answer on your drawing right now! How long did it take?</p>

<p>Layer of water in glass one displaced an equal layer of lemonade in this glass - and where did it go? Right, in glass two.
In other words, there is
as much water in glass one as lemonade in glass two
(top layers in your drawings),
and
as much lemonade in glass one as water in glass two
(bottom layers).</p>

<p>Can you answer the question now?</p>

<p>since the average is 5 and you want 8 add two 3's and an 8 and you get 14.</p>

<ol>
<li>The average (arithmetic mean) of 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 scores of both classes are combined, the average score is 86. What is the value of p/n?</li>
</ol>

<p>The fact that the average 86 is closer to 92 than 70 means that there are more students at 92 than 70, therefore n > p. This is a ratio problem.</p>

<p>The ratio of 92 - 86 : 86 - 70 = 6 : 16 or 3 : 8.</p>

<p>You can actually just do this in your head.</p>

<p>92 - 86 = 6
86 - 70 = 16
3 to 8</p>

<p>It's that simple.</p>

<p>Hey obsessedAndre. Don’t you need to minus the 6 from the 20 because you are looking for the price of the shirt not the discount price so 20-6=14? I don’t know if i am correct so don’t tell me that i am stupid and things like that.</p>