Answer:

✏️VARIATIONS

==============================

Problem: B varies directly to the sum of c and d and inversely to the difference of j and n. B = 3 if c = 8, d = -5, j = 4 and n = 3. What is the value of k?

Solution: Formulate an equation to the given variation.

\begin{gathered} B = k \cdot \frac{c + d}{j - n} \\ \end{gathered}

B=k⋅

j−n

c+d

» Find the value kk or the constant of the variation by substituting the given to the equation.

\begin{gathered} 3 = k \cdot \frac{8 + (\text-5)}{4 - 3} \\ \end{gathered}

3=k⋅

4−3

8+(-5)

\begin{gathered} 3 = k \cdot \frac{3}{1} \\ \end{gathered}

3=k⋅

1

3

\begin{gathered} 3 = k \cdot 3 \\ \end{gathered}

3=k⋅3

\begin{gathered} 3 = 3k \\ \end{gathered}

3=3k

\begin{gathered} \frac{\cancel3k}{\cancel3} = \frac{3}{3} \\ \end{gathered}

3

3

k

=

3

3

k = 1k=1

\therefore∴ The value of kk or the constant of the variation is:

\Large \underline{\boxed{\tt \purple{\,1\,}}}

1

==============================