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?

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IllaP74562 IllaP74562 · Answer 1 · 2022-10-28T01:34:13+02:00

The function of the cost of Pears is:

[tex]\begin{gathered} C=\frac{7}{5}p \\ C=1.4p \end{gathered}[/tex]

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:

[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ By\text{ replacing the values} \\ m=\frac{4-0}{3-0}=\frac{4}{3} \end{gathered}[/tex]

Then, the function of the cost of apples is:

[tex]\begin{gathered} C=\frac{4}{3}a \\ C=1.33a \end{gathered}[/tex]

Where a is the pounds of apples.

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

[tex]\begin{gathered} C_{\text{pears}}=1.4\cdot1=1.4 \\ C_{\text{apples}}=1.33\cdot1=1.33 \end{gathered}[/tex]

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