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. The property tax on a vehicle is $\$ 286.45$. If the vehicle is assessed at a value of $\$ 8500,$ what is the tax rate?

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.
The property tax on a vehicle is $\$ 286.45$. If the vehicle is assessed at a value of $\$ 8500,$ what is the tax rate?

Key Concepts

Initial, Final, and Increase Amounts

This concept involves understanding the roles different amounts play in change problems. The initial amount is the starting value before any modifications occur. The final amount is the value after changes have been applied, and the increase amount is the difference between the final and initial values. Recognizing these distinctions is crucial for setting up equations or proportions correctly in problems involving changes over time.

Percent Change Calculation

Percent change or percent increase is determined by taking the difference between the final and initial values, dividing by the initial value, and then multiplying by 100 to convert it into a percentage. This method quantifies how significantly a value has increased relative to its starting point, and understanding this process is essential for solving problems involving growth or decrease.

Setting Up Proportions

A proportion is a statement that two ratios are equal. In problems involving percentages, setting up a proportion allows you to relate the part (such as the increase amount or tax amount) to the whole (such as the initial amount or assessed value). This method provides a structured way to solve for unknown percentages or rates by ensuring the ratio of the part to the whole is consistent.

Tax Rate Concept

The tax rate is a percentage that represents the amount of tax relative to an assessed value. It is calculated by dividing the tax amount by the assessed value and then converting the resulting fraction into a percentage. This concept allows for an understanding of how property values translate into tax liabilities and is fundamental in solving problems related to tax calculations.

Transcript

00:01 Welcome back to numrod.

00:02 My name is kevin sharak.

00:03 Let's take a look at this question that says that the property tax on a vehicle is $286 .45.

00:11 If the vehicle is assessed at a value of $8 ,500, what is the tax rate? now, there is a warm -up problem that goes along with this that i answered in a problem just before this.

00:21 You can check out problem 21 for the warm -ups.

00:23 So we're just going to jump right in.

00:25 So the property tax is 286 -45.

00:28 Let's write that down.

00:29 Maybe we'll do that as a problem.

00:31 Capital t because i like to use capitals whenever we're talking about dollars just to keep my head straight so this is 286 45 and we're curious what the tax rate is if this is from my car that is 8500 in the value 8500 for the value so maybe i'll call that capital v well let's diagram this out i have 8500 is going to be my entire value of the car and that's going to correspond with 100 percent and then i'm looking for, if i was to knock off $286 here, $286 .45, what is the percentage that would correspond with that? that's the question.

01:28 And so maybe i'll call that little t.

01:32 We'll call that little t.

01:34 So let's begin to set up our proportion.

01:36 I have little t percentage and goes along with 286 .45.

01:45 And then i have 100 % goes along with, 8 ,500.

01:55 Let's make our equal sign there.

01:57 And then we can begin to solve out.

01:59 So i can divide the top and bottom here.

02:00 I'll get t.

02:01 T divided by 100.

02:07 We get this into a decimal place.

02:11 And then i'll get the 100 percent divided by 100 would be 100 over 100...