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. Tina received a raise of $\$ 849.10 .$ If her former salary was $\$ 24,260,$ what was the percent of the increase?

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.
Tina received a raise of $\$ 849.10 .$ If her former salary was $\$ 24,260,$ what was the percent of the increase?

Key Concepts

Percent Increase

Percent increase is a measure that expresses the relative change between the initial amount and the final amount. It is calculated by dividing the increase amount by the initial amount and then multiplying the result by 100 to obtain a percentage.

Proportional Reasoning

Proportional reasoning involves setting up ratios to compare parts of a whole. In the context of percent increase, it means establishing a proportion where the ratio of the increase amount to the initial amount is equivalent to the percent increase over 100, facilitating the process of solving for the unknown percentage.

Increase Amount

The increase amount is the difference between the final and initial amounts. It quantifies the absolute change that has taken place, and when compared to the initial amount, it allows for the calculation of percent increase.

Initial Amount

The initial amount refers to the original or starting value before any changes occur. It serves as the reference point for measuring increases or decreases and is typically used as the denominator when calculating percent change.

Final Amount

The final amount is the value after an increase or decrease has been applied. It represents the end result of a series of transactions or changes and is critical for determining the overall change from the starting point.

Transcript

00:01 Welcome back to numerad.

00:03 My name is kevin sharak.

00:04 Let's consider the question where tina received a raise of $849 .10.

00:10 So important information, let's write that down, $849 and $10.

00:18 And we'll write down that this was a raise just to kind of keep track.

00:22 I think there's going to be a few different things to keep track of here.

00:25 So we say that's her raise.

00:28 If her former salary was $24 ,260, $24 ,260, $24 ,260.

00:36 Was her salary.

00:43 What was the percentage of the increase? so we're looking for the increase.

00:47 And i always like to write that down.

00:48 Let's say increase equals question mark.

00:54 Well, whenever we're looking for a percentage, it's helpful to draw a picture.

01:00 So let's sketch out a rectangle here to represent our initial amount.

01:04 And our initial amount's going to correspond with the salary right here.

01:07 So we can write our salary and say that our salary is going to be the 24 -260.

01:14 And that's going to be everything that's inside this rectangle here.

01:17 And if we want to start relating this to a percentage, it's helpful to think about how much of this rectangle this number makes up.

01:24 Since we made the rectangle based on it, we could call this 100%.

01:29 So it's going to be the 24 -260 goes along with 100%.

01:32 What about this 849 -10? well, that's going to be a raise.

01:36 So it's going to be an addition.

01:38 You can think of it as building on an addition here to this rectangle.

01:41 So we're going to build on some kind of addition.

01:43 And it's going to correspond with this 8, 49, 10.

01:51 Now, if we're looking for the percentage increase, that's going to be this right here.

01:54 Maybe we'll call it p.

01:55 We'll call it p percent.

01:57 And it's going to go along with this increase.

01:58 So we'll make a little note over to the side.

02:02 And now we can begin to do some of our proportion math.

02:05 So we know that this entire rectangle, that is the green and black rectangle combined.

02:09 Maybe we'll call that the red here.

02:11 This entire red is going to have what kind of percent, what percent is going to go along with this well it's going to be the combined total of this 100 percent this p percent so we can write that down we'll say that 100 plus p percent is going to be that red and it's going to go along with the total amount of money that is underneath that shape so we can write that goes along with this 24260 plus the 849 10 okay great now we need something else to relate here that's going to be easy we we could use the p percent, but that might make our math a little bit more difficult than it's needed to.

03:02 You could write that down as being p percent and then relating that to 8, 49, 10.

03:09 And i encourage you to give that a try.

03:11 It's just going to require a little bit more algebraic gymnastics, but i'm going to save us a little bit of time...

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