Question 1163992
.


            Since the problem says  "The dosage usually varies directly as the weight", 

            there is much simpler/shorter way to get the solution/answer.



<pre>
1.  These words mean that the dosages and the weights of patients are proportional.


    So, you can write a proportion


        {{{dosage[1]/weight[1]}}} = {{{dosage[2]/weight[2]}}},     (1)  

    or

        {{{25/160}}} = {{{75/x}}},               (2)


    where x is the unknown dosage under the problem's question.


    From proportion (2),  x = {{{(160*75)/25}}} = 160*3 = 480 mg.     <U>ANSWER</U>



2.  You can also write the base proportion (1) in other form 


        {{{dosage[1]/dosage[2]}}} = {{{weight[1]/weight[2]}}},     (3)  

    or

        {{{160/x}}} = {{{25/75}}}                (4)


    From the proportion (4),  you get the same answer


        x = {{{(160*75)/25}}} = 160*3 = 480 mg.



3.  Instead of using proportions, you can use common sense/reasoning, which tells you that if in the second case 

    the body weight is 3 times as much as in the first case (as you have  {{{75/25}}} = 3), then the dosage in the second case 
    should be 3 times as much as in the first case.
</pre>

Solved.



By doing in this way, &nbsp;you avoid calculating an intermediate coefficient of proportionality &nbsp;"k",

which you do not need and which is simply an auxiliary value.  &nbsp;You directly obtain then the requested/required answer,

making your calculation shorter and the solution more straightforward.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;These straightforward approaches work always and every time, 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;when the problem contains key words &nbsp;"one value varies directly as the second value".


<pre>
The terms 

    -  "one value varies directly as the second value", 
    -  "the values are in direct proportion"   and 
    -  "the values are proportional" 

are synonymous (i.e. EQUIVALENT by their meaning).
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On proportions,  &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/-Proprtions.lesson>Proportions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-word-problems.lesson>Using proportions to solve word problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-word-problems-in-Physics.lesson>Using proportions to solve word problems in Physics</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-solve-Chemistry-problems.lesson>Using proportions to solve Chemistry problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/proportions/lessons/Typical-problems-on-proportions.lesson>Typical problems on proportions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/Using-proportions-to-estimate-the-number-of-fish-in-a-lake.lesson>Using proportions to estimate the number of fish in a lake</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/HOW-TO-algebreze-and-solve-this-problem-using-proportions.lesson>HOW TO algebreze and solve these problems using proportions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/proportions/lessons/Problems-on-proportions-for-mental-solution.lesson>Problems on proportions for mental solution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/proportions/Selected-problems-on-proportions-from-the-archive.lesson>Selected problems on proportions from the archive</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/proportions/lessons/OVERVIEW-of-lessons-on-proportions.lesson>OVERVIEW of lessons on proportions</A>

in this site.


These lessons were written specially for you.  


Read them and become an expert in this area.


Start from the very first lesson.


Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.



/\/\/\/\/\/\/


After reading the comment by Edwin.


<pre>
    Edwin, thank you for your comment which you sent to me.


    Be sure, I always read very attentively every your post . . . 


    Edwin, I think that it is great as you presented your post and your approach, which is a DOMINANT in school teaching.


    I know it VERY WELL, so it is not something new to me.


    But I think that if the student knows BOTH APPROACHES, he (or she) will have GREATER BENEFITS.



    Also, let me add THIS: I think that if the student knows your approach (=standard), but does not know

    my interpretation, it means that he (or she) does not know and does not understand ANYTHING in the subject.


    So, what I explained in my post, is actually a prerequisite for that problem.
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