Question 1163992
<pre>
Ikeyn uses the ratio and proportion method to teach direct variation. It is
correct, but it is not the way variation is taught in schools, nor is it the
way it should be taught.  That's because there are more than just one kind
of variation.  There are several kinds of variation, and all these types are
covered together, so the approaches to them all should show as much similar
as possible.  

Ikleyn should strive to stick to the methods taught in schools rather than
methods we teachers and tutors with more mathematical maturity might think
of.  But a struggling student would not think of them.   
 
Ikleyn should watch videos such as these to learn the standard way variation
is taught in schools.

https://www.youtube.com/watch?v=mwPHQLtKf1Q

https://www.youtube.com/watch?v=nZO5GEaunr4

https://www.youtube.com/watch?v=FpsS0jyZCgA

https://www.youtube.com/watch?v=hCOVwaEoqwA


DIRECT VARIATION:
y varies directly as x                
y varies as x
y is directly proportional to x     

These begin with y = kx 

----------------------- 

INVERSE VARIATION:

y varies inversely as x
y is inversely proportional to x

These begin with y = k/x

-----------------------

JOINT VARIATION:

y varies jointly as x and z           
y is jointly proportional to x and z  

These begin with y = kxz

-----------------------
COMBINED VARIATION:

y varies directly as x and inversely as z
y is directly proportional to x and inversely proportional to z

These begin with y= kx/z

y varies jointly as x and z and inversely as u and v  

These are y = kxz/(uv)

---------------------------------------------



The key words for direct variation are:

"varies as", 
"varies directly as", 
"is proportional to",
"is directly proportional to"

Direct variation problems are of the form:

{{{A=k*B}}}
---------------------------------
The key words for inverse variation are:

"varies inversely as", 
"is inversely proportional to"

Inverse variation problems are of the form:

{{{A=k/B}}}
---------------------------------
The given problem contains the words "varies directly as",
so it is direct variation

{{{A=k*B}}}

{{{Dosage=k*Weight}}}

Choose single alphabet letters for the words:

{{{D=k*W}}}

Substitute the case when BOTH D and W are given

{{{160=k*25}}}

Solve for k, which is to
divide both sides by 25:

{{{160/25=k}}}

{{{6.4=k}}}

Go back to the original equation

{{{D=k*W}}}

Substitute this and the case where only W is given

{{{D=6.4*75}}}

{{{D=480}}}

Edwin</pre>