# Case File: How to Solve Multi-step Problems Involving Percent

Greetings, detectives!

Today, we're putting on our thinking caps to crack a case involving one of the most devious culprits in the world of mathematics: multi-step problems involving percent. Grab your magnifying glass and notebook; it's time to solve the mystery!

## 1. Case Background: Understanding Multi-step Problems Involving Percent

Before we delve into the investigation, let’s brief ourselves on the terms involved:

**Multi-step Problems:**These are problems that require more than one operation or step to find the solution.**Percent:**A ratio or fraction expressed out of \(100\).

## 2. The Investigation: How to Solve Multi-step Problems Involving Percent

Now that we’re armed with the basics, it’s time to dive into the mystery!

### Detective’s Guide: Solving Multi-step Problems Involving Percent

#### Step 1: Understand the Problem

First, read the problem carefully. Identify what you’re asked to find and what information you have.

#### Step 2: Make a Plan

Develop a strategy to solve the problem. This could involve determining percentages, adding or subtracting amounts, or other operations.

#### Step 3: Carry Out the Plan

Execute your strategy. Remember, you might have to perform several steps in order to find the solution.

#### Step 4: Check Your Solution

Finally, review your work to ensure your answer makes sense in the context of the problem.

For example, if you buy a book that costs \($25\) and gets a \(20\)\(\%\) discount, but also has to pay \(5\)\(\%\) sales tax, what’s the final price?

**Understand the Problem:**You need to find the final price after applying a discount and tax to a \($25\) book.**Make a Plan:**First, find the discounted price. Then, apply the tax.**Carry Out the Plan:**- The discount is \(20\)\(\%\) of \($25\), or \($5\). So, the discounted price is \($25\ – $5 = $20\).
- The tax is \(5\)\(\%\) of \($20\), or \($1\). So, the final price is \($20+ $1 = $21\).

- Check Your Solution: A \($25\) book with a \($5\) discount and \($1\) tax should cost \($21\).

Well done, detectives! You’ve solved the mystery of multi-step problems involving percent. Always remember, no case is too tough when you break it down into manageable steps. Keep your wits about you, and happy sleuthing!

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