document.write( "Question 480615: Suppose z varies directly as x and y and inversely as w, and z =8 when x =6, y =5 and w =10. Find z when x =3, y =4 and w = 5. \n" ); document.write( "
Algebra.Com's Answer #329165 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
this reference might be helpful.
\n" ); document.write( "http://www.purplemath.com/modules/variatn.htm
\n" ); document.write( "the wording is important.
\n" ); document.write( "i interpreted your problem as:
\n" ); document.write( "z varies directly as x and y and inversely as w meaning:
\n" ); document.write( "z = kxy/w
\n" ); document.write( "k is the constant of proportionality.
\n" ); document.write( "you are given:
\n" ); document.write( "z = 8
\n" ); document.write( "x = 6
\n" ); document.write( "y = 5
\n" ); document.write( "w = 10
\n" ); document.write( "plug that into the above equation to get:
\n" ); document.write( "8 = (6*5*k)/10
\n" ); document.write( "solve for k to get:
\n" ); document.write( "k = (8*10)/(6*5) = 80/30 = 8/3
\n" ); document.write( "now that you have solved for k, you can go on to solve your problem.
\n" ); document.write( "you use the same formula of:
\n" ); document.write( "z = kxy/w
\n" ); document.write( "the values you are given are:
\n" ); document.write( "x = 3
\n" ); document.write( "y = 4
\n" ); document.write( "w = 5
\n" ); document.write( "the value of k that you previously solved for is:
\n" ); document.write( "k = 8/3
\n" ); document.write( "you want to find z.
\n" ); document.write( "plug those values into your equation to get:
\n" ); document.write( "z = ((8/3) * 3 * 4)/5
\n" ); document.write( "this results in:
\n" ); document.write( "z = (32/5) = 6.4
\n" ); document.write( "you can also do this using ratios.
\n" ); document.write( "this way does not involve the constant of proportionality (k).
\n" ); document.write( "if z is directly proportional to y, this means that:
\n" ); document.write( "z1/z2 = y1/y2
\n" ); document.write( "if z is directly proportional to x, this means that:
\n" ); document.write( "z1/z2 = x1/x2
\n" ); document.write( "if z is inversely proportional to w, this means that:
\n" ); document.write( "z1/z2 = w2/w1
\n" ); document.write( "notice the reverse proportionality when dealing with z and w.
\n" ); document.write( "when you now say that z is directly proportional to x and y and inversely proportional to w, this leads to the equation:
\n" ); document.write( "z1/z2 = (x1*y1*w2)/(x2*y2*w1)
\n" ); document.write( "plug your known values into this equation and solve for the unknown.
\n" ); document.write( "your equation becomes:
\n" ); document.write( "8/z2 = (6*5*5)/(3*4*10)
\n" ); document.write( "simplify this to get:
\n" ); document.write( "8/z2 = 150/120
\n" ); document.write( "multiply both sides of this equation by z2 to get:
\n" ); document.write( "8 = (150/120)*z2
\n" ); document.write( "multiply both sides of this equation by (120/150) to get:
\n" ); document.write( "z2 = 8 * (120/150) = 8 * (12/15) = 8 * (4/5) = (32/5) = 6.4
\n" ); document.write( "you get the same answer.
\n" ); document.write( "the reference gives you good tips on how to translate the words into equation form.
\n" ); document.write( "it also gives you good tips on how to solve these types of equations using the constant of proportionality method.\r
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