Given the equation $\frac{k}{22.8}=6.9$, determine the value of $k$.
The goal is to determine the value of \(k\) from the equation \(\frac{k}{22.8} = 6.9\). This is a linear algebraic equation in one variable, \(k\). To isolate \(k\), we need to perform an inverse operation. Specifically, since \(k\) is divided by \(22.8\), we multiply both sides of the equation by \(22.8\).
To solve for \(k\), we multiply both sides by \(22.8\):
\[ k = 6.9 \times 22.8 \]
Performing the multiplication, we get:
\[ k = 157.32 \]
Comparing our result to the given options:
Our calculated value matches the final option. Thus, the correct value for \(k\) is \(157.32\). The final answer is \(\boxed{157.32}\).
Equations like this are used in various fields, such as chemistry or engineering, when dealing with scaling factors or concentrations. For example, if you are diluting a substance and need to find the total amount based on a known ratio and concentration, you would use this type of algebraic setup to determine the unknown mass or volume. This ensures accuracy when mixing ingredients or chemical compounds to achieve the desired result.