Understanding the Ontario Mathematics Proficiency Test: Solving Percentage Problems

When you're gearing up for the Ontario Mathematics Proficiency Test, it's easy to feel a bit overwhelmed, right? I mean, there’s so many concepts to grasp, from algebraic equations to geometry. Today, we're diving into a topic that often pops up: percentage problems. So let’s break it down in a way that won’t make your head spin!

Imagine you've been given a question that goes something like this: "If a number is increased by 20%, and the result is 120, what was the original number?" Sounds tricky? Not at all! Let’s unravel it together.

At first glance, you might be pondering how to find that original number. The key here is understanding that when we increase a number by a percentage—in this case, 20%—the final result reflects that increase. So, if we consider our original number as ( x ), the relationship here becomes pretty clear.

You see, increasing ( x ) by 20% lands you at 120 which means the final value can be expressed as 120% of that original number. Mathematically, you can write this as:

[ x + 0.2x = 1.2x ]

Now, plug in what we know—we can set ( 1.2x ) equal to 120:

[ 1.2x = 120 ]

To find ( x ), all we have to do is divide both sides of the equation by 1.2. Let’s go ahead and do that:

[ x = \frac{120}{1.2} ]

And voilà! You just calculate that, and what do you get? It’s 100. That’s right, folks! The original number before the percentage increase was indeed 100. Increasing 100 by 20% does lead you back to 120, just as the problem stated.

This technique is really handy, and once you wrap your head around it, you’ll find these types of problems popping up less intimidating. It’s like untangling a set of earphones—you just have to take it step by step.

So next time you encounter a percentage increase question in preparation for the Ontario Mathematics Proficiency Test, remember this simple method. It doesn’t just stop at one question; this foundational understanding allows you to tackle more complex problems with confidence. Knowing how to manipulate percentages not only aids you in exams but in probably every aspect of daily life from budgeting to shopping discounts. You know what? Embracing these challenges will only bolster your math skills. Cheers to that!