Problem 1
Write down the variation equation.
$$ y = \frac k x $$
Use $$ \red{y = 14} $$ and $$ \blue{x = 20} $$ to find the value of $$ k $$. Then write down the updated variation equation.
$$ \begin{align*} \red{14} & = \frac k {\blue{20}}\\[6pt] \red{14}(\blue{20}) & = \frac k {\blue{20}}\cdot \blue {20}\\[6pt] 280 & = \frac k {\cancelred{20}}\cdot \cancelred{20}\\[6pt] k & = 280 \end{align*} $$
The updated variation equation is $$ y = \frac{280} x $$
Determine the value of $$ y $$ when $$ \blue{x = 5} $$.
$$ \begin{align*} y & = \frac{280}{\blue x}\\[6pt] y & = \frac{280}{\blue 5} = 56 \end{align*} $$
$$ y = 56 $$ when $$ x = 5 $$.