DIRECT VARIATION
[tex] \\ \\ [/tex]
If a varies as b and a= 15 when b= 20, find a when b= 32.
[tex] \\ a = kb \\ \\ [/tex]
Evaluate the values
[tex] \\ 15 = k(20) \\ \\ [/tex]
Divide 20 to both sides
[tex] \\ \frac{15}{20} = \frac{k(20)}{20} \\ \\ [/tex]
Cancel both 20 from the right side
[tex] \\ \frac{15}{20} = \frac{k( \cancel{20})}{ \cancel{20}} \\ \\ [/tex]
Simplify
[tex] \\ \boxed{k = \frac{3}{4} } \\ \\ [/tex]
Find the a value when b= 32. Use the k value from the first problem.
[tex] \\ a = kb \\ \\ [/tex]
Evaluate values
[tex] \\ a = ( \frac{3}{4} )(32) \\ \\ [/tex]
Multiply
[tex] \\ \large \green{ \boxed{ \green{ \sf{a = 24}}}} \\ \\ \\ [/tex]
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