Evaluate $\frac{c}{2}-3+\frac{6}{d}$ when $c=14$ and $d=3$.
We are given the expression \(\frac{c}{2} - 3 + \frac{6}{d}\) and need to evaluate it for the specific values \(c = 14\) and \(d = 3\). This involves substituting the given values into the expression and then performing the arithmetic operations in the correct order.
First, substitute \(c = 14\) into the first part of the expression:
\[ \frac{c}{2} = \frac{14}{2} = 7 \]
Next, substitute \(d = 3\) into the last part of the expression:
\[ \frac{6}{d} = \frac{6}{3} = 2 \]
Now, substitute these calculated values back into the original expression:
\[ 7 - 3 + 2 \]
Performing the calculation from left to right:
\[ 7 - 3 = 4 \]
\[ 4 + 2 = 6 \]
Thus, the value of the expression for the given variables is \(6\).
Imagine you are calculating the final cost of a project where \(c\) represents the number of hours spent and \(d\) represents the number of team members. If you have spent \(c = 14\) hours and have \(d = 3\) team members, you might use an expression like \(\frac{c}{2} - 3 + \frac{6}{d}\) to determine a specific efficiency bonus or resource allocation metric. By substituting your known values into such an algebraic expression, you can quickly determine the outcome for your project.