Hello class! Today we're going to be talking about how you can solve percent problems using proportions. The question that we're going to be answering is, how can I use proportions and equations to solve problems involving percents? Well first of all, we need to start off with a few definitions.
A percent proportion is a proportion that specifically can be used to determine percents of numbers. So as you can see, this proportion is comparing the part and the whole to a percent over a hundred. The part in a percent proportion is the number being compared to the whole quantity.
The whole in a percent proportion is the whole quantity or the number to which the part is being compared. Percents are always going to be useful to us whenever we go shopping or are in any situation where tax, tip, or discounts are involved. So for those of you who continue to ask the question, When are we ever going to use this in real life?
Well, percents are a real life way where you see math every day. You can see math at the grocery store when you pay for your total bill. You can see math when you pay for other types of taxes, for clothes, for jewelry, for anything basically that you buy.
You can see percents when you buy a car and the person that sold you the car receives a percentage of how much they sold it to you for. That's called commission. And you also see discounts when you go to buy things in stores as well. The percent proportion, like I said earlier, basically is a proportion that compares the parts.
to the whole. Another way we could say this is is over of. That's going to be helpful when you're reading word problems or problems that are written out in the form of a percent.
For example, 25 percent of 15 is what number? You're looking for those key words, is over of. Here's that percent proportion just filled in with the part and the whole.
And here's a real world example. In a school band of 24 students, 9 students play a brass instrument. What percent of the band members play a brass instrument? Okay, so we need to think about what would represent the part and what would represent the whole. Okay, so 9 of the students out of...
24 members play a brass instrument. So the part would be the 9 students that play a brass instrument out of the whole band. We don't know what percent would go here, so that's going to be represented by the x.
And the percentage is always out of 100 because percentages always are comparing a number to 100. How to find a percent. These are basic percentage problems that you might encounter. For example, what percent of 150 is 45? So as you can see, I rewrote the percent proportion here so I can remember what to fill in.
And then I look at the statement. What percent of 150 is 45? Well, I see of.
with the number 150 next to it. So I'm going to write 150 right at the bottom here. And then is 45. Is goes in the numerator. We don't know what the percentage is, so it's represented by x. And that's always over 100. You end up with 30%.
In the second example, we're learning how to find a part, or the is part of the equation. So, 30% of 150 is what number? So again, rewriting the percent proportion and filling it in. 30%.
Well, I know that 30%, there's a percent sign after the 30, so that's going to go right at the top here over 100. And then, of 150. Of will always go on the bottom. in the denominator and that means that we're looking for the is or the part of the whole. In the last example, how to find a whole. 30% of what number is 45?
So again, we know that the percentage is 30 because there's a percent sign after it. of what number is 45. You see that word is with the number 45 next to it, and we can put that in the numerator. Since we don't know what the hole is, we use the X to represent it.
The sale price of a new pair of Air Jordan basketball shoes is $120. This is 75% of the original price. What was the original price of the Air Jordan basketball shoes?
Hmm, well, we know that there's a percent sign right after this 75. That means I could probably fill in 75 over 100. But what about the is and the of? Well, we know that the basketball shoes are now $120. You need to think about whether that's...
lower or higher than the amount that we had, that the amount that they were originally. So, we know that the shoes were on sale for $120. So, 120 is 75% of what number? So, we're really looking for the of here. You end up with $160.
If the shoes were not on sale, you'd be paying $160 for them. In summary, we can use the percent proportion to find the part, 60% of 50 is what number, the whole, 60% of what number is 30, or the percent, some percent of 50 is 30. In summary, you can use the percent proportion to solve every type of percent problem. You don't need multiple methods to solve percents. As long as you understand how to solve percents with proportions, you'll be all set.
Have a great day!