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If a varies directly as b, and a = 6 when b = 3, find b when a = 2

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DIRECT VARIATION

Problem:

» If a varies directly as b, and a = 6 when b = 3, find b when a = 2

Answer:

  • [tex]\large \bold{b=}\color{hotpink} \: \bold{1 }[/tex]

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Solution:

Write the equation of variation first and substitute the given values of a and b to solve for the k or constant.

  • [tex] \: \: \: \: \: \tt \: a= kb \\ \: \: \: \tt \: \: \: \: \: \:6= k(3) \\ \: \: \: \tt \: k = \frac{6}{3} \\ \tt \: \: \: k = \blue{2}[/tex]

Since, the constant of variation (k) is 2. Therefore, the equation of variation is:

  • [tex]\underline{ \boxed{ \tt{a = 2b}}} [/tex]

Then, using the equation of variation above, find the unknown value of b when a = 2.

  • [tex] \: \: \: \: \: \: \: \tt a= 2b\\ \: \: \: \: \: \: \: \tt 2 = 2b\\ \: \: \: \: \: \tt \: b= \frac{2}{2} \\ \: \tt \: \: \: \: \: \: \: b = \underline{ \boxed{ \blue{ \tt1}}}[/tex]

Hence, the value of b is 1.

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