# Total Revenue

You know that pile of DVDs you have in your house, collecting dust because you don’t watch them anymore? Imagine you sell them on eBay to make a few bucks. How does that sound?

Now I bet you are thinking… the more DVDs I sell, the more I will get paid. Am I close? This thought comes naturally and, odds are, you didn’t even notice you were doing this, it just made sense. Well, you were calculating Total Revenue.

Suppose you sell 10 DVDs at a price of\$5 each. Then, you will earn

\$5 x 10 = \$50

Don’t get all happy just yet! This is actually less than if you sell more DVDs, say 20 DVDs, in which case you will earn

\$5 x 20 = \$100

Alternatively, you could also get a Ben Franklin bill charming your wallet if you sold the same 10 DVDs but at a higher price, \$10,

\$10 x 10 = \$100

To calculate your Total Revenue, TR, you are simply multiplying price, P, by quantity, Q:

Total Revenue = Price x Quantity

or

TR = P x Q

Naturally, we could be given Total Revenue and Price and be asked to calculate Quantity, or we could be given Total Revenue and Quantity and be asked to calculate Price.

For example, suppose you earned \$36 when you sold your DVDs for \$2 each, this means you sold 18 DVDs:

18 = 36 / 2

Alternatively, if you earned \$40 when you sold 10 DVDs, and let’s just assume, for simplicity’s sake, that you sold them all the same price, this means you sold them for \$4 each:

4 = 40 /4

In these cases we simply divided TR by P, or we’d divide TR by Q, respectively:

Q = TR / P

or

P = TR / Q

#### Pause & Reflect: Practice Questions

Thinking about these questions & writing the answers will help you to pause and reflect. This will show you if you are keeping up or if you missed a detail and should go back to check it out.

You sell 20 keychains at a price of \$2 each. What is your Total Revenue?

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If you sell 10 pens at a price of \$8 each, what is your Total Revenue?

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How many soccer balls must you sell at a price of \$10 each to earn \$400 of Total Revenue?

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Your Total Revenue from mowing lawns is \$120. You mowed 10 lawns this weekend. How much did you receive per lawn?

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## Graphing Total Revenue

So far, we’ve seen that Total Revenue depends on two things, price and quantity. Graphically, the result of this multiplication is the area of a rectangle, where the base is the quantity sold and the height is the price per unit. Let’s get to it.

Begin by noting that selling a given quantity, Q, at a given price, P, is simply a point on a graph. Let’s bring an example here.

Suppose you sell 30 DVDs at a price of \$4 each. You represent that as follows in our typical graph, where price is on the y-axis and quantity is on the x-axis:

The revenue that you earn from that sale is

TR = \$4 x 30 = \$120

Graphically, this is the area of a rectangle, where the base of the rectangle is quantity, 30, and the height is the price, \$4; we like to represent this with a shaded area:

#### Pause & Reflect: Practice Questions

Thinking about these questions & writing the answers will help you to pause and reflect. This will show you if you are keeping up or if you missed a detail and should go back to check it out.

Use the graphs below to graph the Total Revenues you calculated in the previous exercise.

You sell 20 keychains at a price of \$2 each. What is your Total Revenue?

If you sell 10 pens at a price of \$8 each, what is your Total Revenue?

How many soccer balls must you sell at a price of \$10 each to earn \$400 of Total Revenue?

Your Total Revenue from mowing lawns is \$120. You mowed 10 lawns this weekend. How much did you receive per lawn?