Q45. - Algebra 1

Question

The table shows the cost of picking your own strawberries at a farm.

Number of Pounds	1	2	3	4
Total Cost ($)	1.25	2.50	3.75	5.00

a. Graph the data.

b. Write an equation in function notation to describe this relationship.

c. How much would it cost to pick 6 pounds of strawberries?

Step-by-Step Solution

Answer

a. The graph of the data is:

b. The equation in function notation to describe this relationship is $y=1.25x$.

c. The cost to pick 6 pounds of strawberries is $7.5.

Part a. Step 1. Observe the table.

The given table is:

Part a. Step 2. Graph the data.

The graph of the data is:

Part b. Step 1. Observe the table and find the differences between number of pounds and total cost.

Calculate the difference between the number of pounds and total cost.

From the above table it can be noticed that the difference between the number of pounds is 1 and the difference between the total cost is 1.25.

 

This implies the value of constant of variation (k) is given by:

$$\begin{gathered} k=\frac{1.25}{1} \\ =1.25 \end{gathered}$$

Part b. Step 2. Find an equation in function notation to describe this relationship.

As, the value of k is 1.25. Therefore, the equation in function notation to describe this relationship is given by:

 $$\begin{gathered} y=kx \\ y=1.25x \end{gathered}$$

Where x and y represents the number of pounds and Total cost respectively.

Part c. Step 1. Write the equation expressing relation between the number of pounds and total cost.

The equation expressing relation between the number of pounds and total cost is:

$y=1.25x$ 

Where x and y represents the number of pounds and Total cost respectively.

Part c. Step 2. Find the cost to pick 6 pounds of strawberries.

The number of pounds is 6. Therefore, the value of x is 6.

The cost to pick 6 pounds of strawberries is given by:

 $$\begin{gathered} y=1.25x \\ =1.25\left(6\right) \\ =7.5 \end{gathered}$$

Therefore, the cost to pick 6 pounds of strawberries is $7.5.