# 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

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?

1. Understand the Problem: You need to find the final price after applying a discount and tax to a $$25$$ book.
2. Make a Plan: First, find the discounted price. Then, apply the tax.
3. 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 $$20+ 1 = 21$$.
4. 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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