## Tips for Solving More Complex Percent Problems

You’ve mastered the basics—finding percentages of numbers, determining unknown percentages between amounts, and calculating wholes from percentages. Now it’s time to level up your skills to master multi-step percent problem-solving.

When word problems involve multiple percentages taken at different times, various unknowns, and real-world scenarios like discounts upon discounts, it’s easy to get overwhelmed. Luckily, there are straightforward techniques you can apply to break down and solve even the most convoluted percent questions.

### 1. Carefully Read the Entire Problem

Before blindly jumping into calculations when facing a wordy percent problem, first carefully read the entire question from start to finish. Key details could be buried in the middle or end that provide clues on how to proceed.

Highlight or underline numbers and variables you know as well as what the actual unknown is that you need to solve for. Having a clear picture sets you up for success.

### 2. Break It Down Step-By-Step

Now that you’ve identified the key components of the complex question, break it down into logical steps. Write out what needs to happen first, second, etc., to ultimately get to the solution.

Let’s follow this example:

A clothing store is having a sale. They first discount the original price by 30%. After applying the 30% discount, they take an additional 15% off the newly discounted price. If the original price of a jacket was $100, what would be the final price after applying both discounts?

Follow these steps to solve complex multi-step problems like this one:

- Take 30% of the original price
- Subtract this discount
- New discounted price
- Take 15% of the discounted price
- Subtract this amount to get the final price

Step |
Calculation |

Original Price |
$100 |

Take 30% of the original price |
$100 x 0.3 = $30 |

Subtract this discount from the original price |
$100 - $30 = $70 (New discounted price) |

Take 15% of the discounted price |
$70 x 0.15 = $10.50 |

Thinking through the precise order of operations helps you systematically work through multi-layered problems.

### 3. Start Simple

If a problem still seems confusing after breaking it down, try substituting simpler numbers to walk through a basic version. For example, instead of a sweater originally $100, try an item originally $10 instead. Or instead of 40% off, use 10% off.

Going through rounds with clean hypothetical numbers provides a clearer picture of what mathematical operations and sequence of steps will lead to the solution. The process needed often clicks better when practiced in initial straightforward cases.

### 4. Double-Check Your Work

Especially on longer, multi-step problems, it’s important to double-check that your final number makes logical sense given the question’s parameters.

For example, if you solved for a total discounted price after several rounds of percent-off coupons, does the final number seem reasonable? Is it at least smaller than the original pre-discount amount?

Scanning back through to confirm you applied discounts properly and didn’t mix up any minus signs prevents careless errors.

Let's apply these strategies to some more advanced questions:

Question |
Answer |

The retail price of a sweater is $50. First, the store applies a 30% markdown on the sweater during a back-to-school sale. Then, they take an additional 15% student discount at checkout. What is the final price of the sweater? |
Original price: $50 30% of $50 = 0.3 * $50 = $15 off New price after 30% markdown = $50 - $15 = $35 Now take 15% off $35 for the student discount 0.15 * $35 = $5.25 Final price after additional 15% off = $35 - $5.25 = $29.75 The final price of the sweater is $29.75 |

At a restaurant, the original bill before tax and tip was $60. A 20% tip was added to the original bill amount. Then an 8% sales tax was applied to the new total, including the tip. What was the final total bill? |
Original bill: $60 Take 20% of $60 for tip: 0.2 * $60 = $12 Bill + Tip = $60 + $12 = $72 Take 8% of $72 for tax: 0.08 * $72 = $5.76 $72 + $5.76 = $77.76 Therefore, the final total bill was $77.76 |

These examples reinforce having a logical process to break down more complex questions. Applying targeted percent strategies step-by-step helps you solve these problems with ease!