Question

Mike sells grapes at a farmers market. Each pound of grapes sells for the same amount. The table below shows the total prices for different numbers of pounds of grapes sold. Grapes Number of Pounds Sold Total Price ($) 2$4.504$9.0010$22.50 A. Write an equation that describes the relationship between the number of pounds of grapes sold(x) and the total price (y), in dollars. Mike also sells red peppers at the farmers market. The equation below can be used to find the total price (p) in dollars of r pounds of red peppers. p = 1.80r B. What is the total price, in dollars, of 17 pounds of red peppers? Explain what the 1.80 represents in the context of the situation. The farmer decides to increase the price per pound of the grapes. A graph is created to represent both the original equation from Part A and a new equation based on the increased price per pound of the grapes. C. Thinking about what this graph would look like, explain why the graphs representing the equations will share one point even though the prices per pound are different.

Answer 1

Given the table:

Number of pounds sold Total price $

2 $4.50

4 $9.00

10 $22.50

Let's solve for the following:

• A. Write an equation that describes the relationship between the number of pounds of grapes sold(x) and the total price (y), in dollars.

Apply the slope intercept form of a linear equation: y = mx + b

Where m is the average rate of change(slope) and b is the y-intercept.

To find the slope, m apply the slpe formula:

`m=(y2-y1)/(x2-x1)`

Take two points from the table:

(x1, y1) ==> (2, 4.50)

(x2, y2) ==> (4, 9.00)

Thus, we have:

`\begin{gathered} m=(9.00-4.50)/(4-2) \\ \\ m=(4.50)/(2) \\ \\ m=2.25 \end{gathered}`

Since each of the grapes sells for the same amount, the value of b will be = 0.

Therefore, the equation that describes the relationship is:

`y=2.25x`

• B. Given the equation: p = 1.80r

• i) To find the total price of 17 red peppers, substitute 17 for r and evaluate:

`\begin{gathered} p=1.80r \\ \\ p=1.80(17) \\ \\ p=30.6 \end{gathered}`

Therefore, the total price, in dollars, of 17 pounds of red peppers is $30.60

• ii) Explain what the 1.80 represents in the context of the situation.

1.80 in this equation represents the price of 1 pound of red pepper. It can also be called the average price of pound of red peppers.