Verified Answer :

  • Evaluate the sum within the parentheses: \((25+5) = 30\).
  • Multiply the result by 3: \(30 \times 3 = 90\).
  • Subtract 13 from the product: \(90 - 13 = 77\).
  • The final result is \(\boxed{77}\).

Explanation

  1. Problem Analysis and Order of Operations

The expression to simplify is \((25+5) \times 3 - 13\). To solve this correctly, we must adhere to the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This systematic approach ensures that we prioritize the operations in the correct order to arrive at the consistent result.

  1. Evaluating Parentheses

First, we resolve the operation inside the parentheses. We have \((25+5) = 30\). Substituting this back into the expression, we now have \(30 \times 3 - 13\).

  1. Performing Multiplication

Next, we perform the multiplication step. Multiplying \(30\) by \(3\) gives us \(30 \times 3 = 90\). The expression now simplifies to \(90 - 13\).

  1. Final Subtraction and Result

Finally, we complete the last step by performing the subtraction. Taking \(13\) away from \(90\), we calculate \(90 - 13 = 77\). Thus, the simplified value of the expression is \(77\).

Examples

Imagine you are buying supplies for a project. You need to buy 3 packs of pens, where each pack contains 25 blue pens and 5 red pens. After calculating the total number of pens, you realize 13 of them are defective and must be removed. The total number of pens you have left is represented by the expression \((25+5) \times 3 - 13\). Following the correct order of operations ensures you know exactly how many functional pens you have for your project.

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