Problem:
The variables d varies jointly as the variables a, b and varies inversely as c. When a = 12, b = 21, c = 105 we have d = 60. What is the value of d when a = 32, b = 9,and c = 8?
Solution:
[tex]\[d = \frac{{kab}}{c}\][/tex] ; k = constant of variation
[tex]\[\begin{array}{l}60 = \frac{{k(12)(21)}}{{105}}\\\\60(105) = 252k\\\\6300 = 252k\\\\\frac{{6300}}{{252}} = \frac{{252k}}{{252}}\\\\k = \frac{{6300}}{{252}}\\\\k = 25\\\end{array}\][/tex]
[tex]\[\begin{array}{l}d = \frac{{kab}}{c}\\\\d = \frac{{(25)(32)(9)}}{8}\\\\d = \frac{{7200}}{8}\\\\d = 900\end{array}\][/tex]
Answer:
d = 900
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