Evaluate $5 x y$ if $x=2$ and $y=4$.
The problem asks us to evaluate the expression \(5xy\) given that \(x=2\) and \(y=4\). This is a basic algebraic substitution and evaluation task. We need to replace the variables \(x\) and \(y\) with their provided values and perform the arithmetic multiplication to find the resulting value.
We substitute \(x=2\) and \(y=4\) into the expression \(5xy\):
\[5xy = 5 \cdot (2) \cdot (4)\]
Now, we perform the multiplication step-by-step. First, multiply 5 and 2:
\[5 \cdot 2 = 10\]
Next, multiply the result by 4:
\[10 \cdot 4 = 40\]
Thus, the value of the expression is 40.
The evaluation of the algebraic expression \(5xy\) for the given values \(x=2\) and \(y=4\) results in a final value of 40. We have successfully substituted the variables and computed the product. Therefore, the result is \(\boxed{40}\).
In real-life scenarios, calculating expressions is essential for budgeting or resource allocation. For instance, if you are planning to buy 5 items of each of two different types, and you know the cost of the first item type is \$2 and the second item type is \$4, calculating the total cost follows the same principle: \(5 \cdot 2 \cdot 4 = \$40\). This demonstrates how algebraic substitution simplifies solving practical arithmetic problems.