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 company's cost of production for one unit of a product was $\$ 328.50 .$ After taking some cost-cutting measures, the company was able to reduce the cost of production by $\$ 14.50$ per unit. What is the percent of decrease in cost?

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 company's cost of production for one unit of a product was $\$ 328.50 .$ After taking some cost-cutting measures, the company was able to reduce the cost of production by $\$ 14.50$ per unit. What is the percent of decrease in cost?

Key Concepts

Proportion Equation Setup

Setting up a proportion involves forming an equation that relates the change to the initial amount in terms of percent. Typically, the change divided by the initial amount is set equal to the percent change divided by 100. This proportional reasoning helps solve for the unknown percentage efficiently.

Initial Amount

The initial amount is the starting value before any changes occur. It serves as the reference point when comparing how much a quantity has increased or decreased over time, making it essential for calculating percent changes where the original value acts as the denominator.

Final Amount

The final amount is the value after a change has been applied. It reflects the new state after an increase or decrease and, when compared to the initial amount, allows for the determination of the adjustment's magnitude.

Change Amount

The change amount represents the difference between the final and initial values. Whether it signifies an increase or a decrease, this value is critical because it quantifies the amount by which the original quantity has changed and serves as the numerator in percent change calculations.

Percent Change Calculation

Percent change is obtained by dividing the change amount by the initial amount and then multiplying the result by 100. This calculation expresses the relative change as a percentage, enabling comparison across different scales and contexts.

Transcript

00:01 Hello, welcome back to numorod.

00:02 My name is kevin sharak.

00:03 Let's take a look at this question here.

00:05 So we have a company's cost of production is one unit of product being $328 .50.

00:12 So let's just sketch out our thoughts here.

00:14 We have one unit that corresponds with $3 .28.

00:26 And then what else do we have? after taking some cost cutting measures, the company was able to reduce the cost by $14 .50.

00:33 Okay, so we can say that we had, this is maybe our cost.

00:38 And then i have some kind of a reduction.

00:42 And i reduced it by 1450.

00:48 And the question asks for, what is the percentage decreased of the cost? okay, well, let's take a moment and see if we can diagram this out.

00:55 Maybe we'll make this part equal to blue, and we'll make this part equal to green.

01:00 So let's take my initial cost and let's sketch it out here, maybe as a rectangle.

01:06 So i have $328 .50 that goes along with this rectangle.

01:12 And notice that this question is asking us about the cost and how we change the costs.

01:16 So this one unit over here is not playing a role in our rectangle.

01:21 It kind of goes along with our rectangle, but the number one doesn't go along with our rectangle if our rectangle is about cost.

01:29 Because what i'm then going to do is i'm going to try to reduce this cost, right? so i'm going to chop away at this rectangle.

01:34 And the amount that i'm chopping away at this rectangle is this $14 .50.

01:42 Okay, well, perhaps we need some percentages to go along with it.

01:45 Was the full rectangle the full rectangle was this 100%.

01:50 And then we're trying to figure out the percent that's the reduction.

01:54 So that goes in right here, this little p percent.

01:57 And so we can write over here to the side to keep track of things.

01:59 P percent is going to be equal to the percent reduction.

02:08 Well, let's begin to set up some relationships here.

02:12 Perhaps we will relate the numbers on the top with the numbers on the bottom.

02:16 So it'd be $328 .50.

02:19 Sense and maybe just for symmetry this time i will keep the dollars on top i can organize these fractions just about any way that keeps that i want so long as i keep similar elements on the tops and bottoms of these fractions so i can put the 100 % in the bottom and then i have a p % that's going to come down here okay so let's begin to do some simplification shall we the first thing we can do is we could rewrite maybe this 100 % as its decimal form which would just be the number one, right? you get a number one by moving this decimal point over two times.

02:59 So 32850 divided by 100 % is just going to be 328 .50 divided by 1, or the unchanged 32850.

03:11 On the left -hand side, you've got 1450 divided by p %.

03:15 We're going to need to get that p % out of the bottom there, out of the denominator.

03:21 So what could we do to cancel something on the denominator? we could multiply both sides by that value, because it's a number of the denominator...

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