Verified Answer :

  • Substitute \(y = 6\) into the first term to get \(\frac{3}{2} \times 6 = 9\).
  • Substitute \(z = 3\) into the third term to get \(\frac{5}{3} \times 3 = 5\).
  • Combine these results with the constant term: \(9 - 3 + 5\).
  • The final evaluated result is \(\boxed{11}\).

Explanation

  1. Understanding the Problem

The problem asks to evaluate the expression \(\frac{3}{2} y - 3 + \frac{5}{3} z\) with the given values \(y = 6\) and \(z = 3\). To solve this, we will substitute these numerical values directly into the expression and perform the necessary arithmetic operations step by step.

  1. Substituting and Simplifying Terms

First, we substitute \(y = 6\) into the term \(\frac{3}{2} y\):
\[\frac{3}{2} \times 6 = \frac{3 \times 6}{2} = \frac{18}{2} = 9.\]
Next, we substitute \(z = 3\) into the term \(\frac{5}{3} z\):
\[\frac{5}{3} \times 3 = \frac{5 \times 3}{3} = 5.\]

  1. Final Evaluation

Now that we have evaluated the individual terms, we substitute them back into the full expression \(\frac{3}{2} y - 3 + \frac{5}{3} z\):
\[9 - 3 + 5.\]
Performing the subtraction:
\[9 - 3 = 6.\]
Finally, adding the last term:
\[6 + 5 = 11.\]
Thus, the final value of the expression is \(\boxed{11}\).

Examples

Suppose you are calculating your total weekly savings. You save a certain amount based on your hourly wage (\(y=6\) hours) and a separate bonus based on extra tasks completed (\(z=3\) tasks). If your base wage contribution is \(\frac{3}{2} y\), your fixed costs are \(3\), and your bonus per task is \(\frac{5}{3} z\), the expression \(\frac{3}{2} y - 3 + \frac{5}{3} z\) helps you determine your net savings for the week. By substituting the values, you can quickly find your total financial outcome.