One month a business earns 40,000 in revenue. The next...

One month a business earns $\$ 40,000$ in revenue. The next month the business increases the revenue55000. a. Is $\$ 40,000$ an initial amount, a final amount, or an increase amount? b. Is $\$ 5000$ an initial amount, a final amount, or an increase amount? c. With the information given, to find the percent of increase, do you need to subtract prior to setting up the proportion? Why or why not? d. Write a proportion that can be used to find the percent of increase. A salesperson says that he can take $\$ 1512$ off the price of a car. If the initial price is $\$ 18,900,$ what is the percent of decrease?

One month a business earns $\$ 40,000$ in revenue. The next month the business increases the revenue55000.
a. Is $\$ 40,000$ an initial amount, a final amount, or an increase amount?
b. Is $\$ 5000$ an initial amount, a final amount, or an increase amount?
c. With the information given, to find the percent of increase, do you need to subtract prior to setting up the proportion? Why or why not?
d. Write a proportion that can be used to find the percent of increase.
A salesperson says that he can take $\$ 1512$ off the price of a car. If the initial price is $\$ 18,900,$ what is the percent of decrease?

Key Concepts

Setting Up and Solving Proportions

This concept involves creating a mathematical relationship between the change (whether increase or decrease) and the initial amount. By establishing a proportion, one can solve for unknown percentages or amounts, making it a fundamental approach to solving problems related to percentage changes.

Percent Change Calculation

Percent change is a way to express the change as a fraction of the initial amount, converted into a percentage. It involves setting up a proportion where the increase or decrease amount is divided by the initial amount and then multiplied by 100, providing a standardized measure of change.

Final Amount

The final amount is the value after a change has been applied, whether that change is an increase or a decrease. This value is used along with the initial amount to determine the magnitude of the change.

Initial Amount

The initial amount is the starting value before any changes occur. In percentage change problems, this value serves as the reference point for calculating how much the amount has increased or decreased relative to its original value.

Increase/Decrease Amount

This represents the absolute difference between the final amount and the initial amount. It provides the numerical value of the change, which is essential for calculating the percentage change by comparing it to the initial amount.

Transcript

00:01 All right, welcome back to numerad.

00:01 My name is kevin shrock.

00:03 Let's consider a question where we have, let's see, a salesperson who says that they can take $1 ,512 off the price of a car.

00:15 It's quite nice.

00:16 All right, so $1 ,512 can be taken off of the car.

00:28 If the initial price is $18 ,900, so write $18 ,900 is the initial.

00:40 Then what is the percentage decrease? okay, so we're going to be working with percentages.

00:44 Again, it's helpful to diagram out percentages.

00:47 So let's take a moment here and make a rectangle.

00:50 And this rectangle is going to represent our initial value.

00:53 So our initial value is going to be this $18 ,900 that goes along with a percentage.

01:02 Well, it's going to be our entire rectangle, so we can write that as 100%.

01:07 Okay.

01:08 Now let's talk about what's happening with this $1 ,512.

01:11 I'm taking this amount off of, of the car.

01:15 So i'm almost chopping away at this rectangle and removing a lot of this, taking a lot of that away.

01:21 And how much is that blue? we said it was $1 ,512.

01:28 The question is, is what is the percentage that we took off of this? what is that p %? and that's our question right here.

01:35 So we come out over here, that p % is gonna be equal to question mark.

01:40 Well, again, with proportions, all you need to do is relate some values that you think are of interest.

01:44 So for example, we could do the 100, and we could relate it to the $18 ,900.

01:58 All we need to do is to make sure that we line up whatever's on the numerator with its similar partner you'll say or the similar property for our other relation.

02:08 So for example, maybe we want to consider the blue part.

02:12 Well, that means we're still going to have to put the percentage on top so we could put p percent on top and the 1 ,512 on the bottom.

02:22 Okay.

02:22 Well, what can we do here to solve out? we could solve everything that's over here.

02:29 That would be quite easy.

02:32 And then maybe we could divide over or multiply over the number on the denominator.

02:36 Let's see what that looks like.

02:38 All right.

02:38 So what's 100 % divided by 18 ,900? maybe a little bit challenging.

02:44 We could make that percentage instead into a decimal.

02:47 So 100%, if we just move that decimal place over two times, it's going to be the same as the number one.

02:52 So i've got 1 over 18 ,900 is equal to p % over 1 ,512.

03:08 Well, i'd like to get the p % alone...

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