Question

The graph above shows the cost, in dollars, of apples as a function of the number of pounds of apples purchased at a particular grocery store. The equation above defines the cost C, in dollars, for p pounds of pears at the same store. Which of the following statements accurately compares the cost per pound of apples and the cost per pound of pears at this store?

Answer 1

The function of the cost of Pears is:

`\begin{gathered} C=(7)/(5)p \\ C=1.4p \end{gathered}`

Now, with the graph, we can find the function of the Cost of apples, let's find the slope.

In the graph we can identify the next two points: (0,0) and (3,4).

The formula for the slope is:

`\begin{gathered} m=(y2-y1)/(x2-x1) \\ By\text{ replacing the values} \\ m=(4-0)/(3-0)=(4)/(3) \end{gathered}`

Then, the function of the cost of apples is:

`\begin{gathered} C=(4)/(3)a \\ C=1.33a \end{gathered}`

Where a is the pounds of apples.

Then the cost of 1 pound of pears and the cost of 1 pound of apples is:

`\begin{gathered} C_{\text{pears}}=1.4\cdot1=1.4 \\ C_{\text{apples}}=1.33\cdot1=1.33 \end{gathered}`

Then, apples cost approximately $1.4-$1.33=$0.07 less per pound than pears do.