Each small square in the grid for this graph has one side equal to 1 pound of nails and one side equal to 1 dollar per pound. The area of one small square is therefore blank.

Question

There are blank small squares in the purple shaded rectangle.

On this graph, the area of the purple rectangle corresponds to:
Royal Hardware’s revenue from selling nails, measured in dollars
The price of the nails, measured in dollars per pound
The number of nails that Royal Hardware sold, measured in pounds
None of these—the area has no meaning

Now suppose Royal Hardware raises its price to $7.00 per pound of nails. As a result, it now sells 5 pounds of nails.

Use the blue rectangle to draw the area that corresponds to the new price and quantity.
Did raising the price of nails increase Royal Hardware’s revenue?
Yes
No

Answer 1

To determine the area of one small square in the grid, we need to calculate its area, which is given by the product of its two sides:

\[ \text{Area of one small square} = \text{side}_1 \times \text{side}_2 = 1 , \text{pound} \times 1 , \text{dollar per pound} = 1 , \text{pound dollar} \]

Therefore, the area of one small square is 1 pound dollar.

Now let’s find out how many small squares there are in the purple shaded rectangle. The area of the purple rectangle typically corresponds to someone’s revenue (in this case, Royal Hardware’s revenue from selling nails), measured in dollars. However, without specific dimensions or additional context, we cannot calculate how many small squares are in the purple rectangle.

Next, let’s analyze the situation when Royal Hardware raises its price to $7.00 per pound and sells 5 pounds of nails.

To calculate the revenue at this new price: \[ \text{Revenue} = \text{Price per pound} \times \text{Pounds sold} = 7 , \text{dollars per pound} \times 5 , \text{pounds} = 35 , \text{dollars} \]

This revenue can be represented as a rectangle where one side measures the new price of the nails ($7.00) and the other side measures the quantity sold (5 pounds). The area of this new blue rectangle represents Royal Hardware’s revenue under the new pricing structure.

Now, to determine if raising the price of nails increased Royal Hardware’s revenue, we would need to compare this new revenue of $35.00 to their previous revenue (which would need to be calculated based on the earlier price and quantity sold). Assuming Royal Hardware sold more pounds at a lower price previously or if their previous revenue was lower than $35.00, then raising the price would indeed have resulted in increased revenue.

If we assume their previous price and quantity sold resulted in revenue less than $35.00, then: Yes, raising the price of nails increased Royal Hardware’s revenue.

If they sold fewer pounds or at a price which resulted in total revenue less than $35.00, the answer remains Yes.

However, if they previously had a better revenue situation with a different price and quantity combination than their current state, it could be No.

Without that previous context, the generic conclusion is: Yes, raising the price of nails increased Royal Hardware's revenue if comparing to a lower price point.

Lastly, you can represent this abstraction graphically using a simple blue rectangle in the grid with dimensions reflecting the new price of $7 (height) and the pounds sold (width) as 5 pounds.