Welcome back to Multi-Step Percent Problems! You have already worked through three of the five lessons in this course, so you are well past the halfway mark. Great progress!

So far, we have practiced choosing the correct base for a percent calculation, recovering an original amount after a percent change, and applying consecutive percent changes one after another. In each of those lessons, every adjustment was a percentage. In real life, though, not every adjustment is a percentage. Sometimes a transaction mixes a percent-based step with a flat dollar amount — think of a store coupon for 20% off followed by a $5 delivery fee, or a $10 loyalty credit followed by 8% sales tax. This lesson focuses on exactly that kind of mix: one percent adjustment and one fixed-dollar adjustment, applied in a stated order.

Before we dive into calculations, let's build some intuition. When two adjustments are both fixed dollar amounts, order does not matter. Subtracting $5 and then subtracting $10 gives the same result as subtracting $10 first. Similarly, as you saw in the previous lesson on consecutive percent changes, the order of two percent multiplications does not change the final product.

However, the moment we combine a percent step with a fixed-dollar step, order does matter. A percentage is calculated on whatever amount exists at that moment, so the dollar value it produces depends on when it is applied. A fixed-dollar adjustment, on the other hand, always adds or subtracts the same number regardless of timing. This single difference is the key idea for the entire lesson.

Let's start with a common pattern: apply the percent change first, then apply the fixed-dollar change.

Example 1. A jacket costs $80. A store offers 25% off, and there is a flat $6 shipping fee added afterward.

1. Percent step first. The discount is 25% of $80:

The price after the discount is $80 − $20 = $60.

1. Fixed-dollar step second. Add the $6 shipping fee:

Now let's reverse the order: the fixed-dollar change happens first, and the percent change is applied to the updated amount.

Example 2. A restaurant bill is $60. A $10 gift card is applied first, and then an 18% tip is calculated on the remaining balance.

1. Fixed-dollar step first. Subtract the gift card:

The balance after the gift card is $50.

1. Percent step second. The tip is 18% of $50:

To really drive the point home, let's take one scenario and compute it both ways. A laptop costs $500. There is a 10% discount and a flat $30 setup fee.

The two orders produce different totals: $480 versus $477. The difference is only $3 here, but in larger transactions it can be significant. The takeaway is straightforward: always follow the order stated in the problem.

Once you are comfortable with the two-step logic, you can combine everything into a single expression. The key is to translate each step into its arithmetic operation, in order from left to right.

For the jacket example (25% off $80, then add $6):

Even though the math in each individual step is straightforward, two mistakes come up often:

• Applying the percent to the wrong amount. If the fixed-dollar step happens first, the percent must be calculated on the adjusted amount, not the original. Always ask yourself: "What is the current amount right now?"
• Mixing up addition and subtraction. A discount or credit reduces the amount, while a fee, tip, or tax increases it. Before calculating, decide whether each step makes the total go up or down.

A good habit is to label each step clearly, just as we did in the examples above. Writing "after discount" or "after fee" next to each intermediate result helps you stay on track and catch errors before they snowball.

In this lesson, you learned how to handle problems that combine one percent adjustment with one fixed-dollar adjustment. The central takeaway is that order matters: the percent step produces a different dollar amount depending on whether it is applied before or after the fixed-dollar step, so you must always follow the sequence stated in the problem. With a clear two-step approach — label, calculate, move on — these problems become manageable and even routine.

Up next, you will put this skill into practice with a set of hands-on exercises that walk you through both orderings in a variety of realistic scenarios. You will fill in partially worked examples, compute final amounts on your own, and write out your reasoning for a real shopping situation. Jump in and see how quickly you can master the mix!