Question

a group of friends chartered a deep - sea fishing boat out of destin, fl. the given graph represents the total cost, in dollars, of the trip as a function of the number of people going.
the group is trying to determine what the price difference would be per passenger if 10 of them go on the trip versus if 16 of them go on the trip. what is the difference in price per passenger for a group of 16 versus a group of 10?
$46.25
$36.25
$26.25
$56.25

Explanation:

Step1: Find total cost for 10 people

From the graph, total cost for 10 people is $\$1700$.

Step2: Calculate cost per person for 10

$\text{Cost per person} = \frac{1700}{10} = 170$

Step3: Find total cost for 16 people

From the graph, total cost for 16 people is $\$2500$.

Step4: Calculate cost per person for 16

$\text{Cost per person} = \frac{2500}{16} = 156.25$

Step5: Compute the difference

$\text{Difference} = 170 - 156.25 = 13.75$
Wait, correction: Recheck graph values. For 10 people, total cost is $\$900$? No, re-verify: The horizontal segment is $\$900$ for 0-5 people, then rises to $\$1700$ at 15 people. For 10 people, interpolate the linear segment:
The linear part is from (5, 900) to (15, 1700). Slope $m=\frac{1700-900}{15-5}=80$. Equation: $y-900=80(x-5)$. For $x=10$: $y=900+80(5)=900+400=1300$.

Step1 (corrected): Total cost for 10 people

$y = 1300$

Step2 (corrected): Cost per 10 people

$\frac{1300}{10}=130$

Step3: Total cost for 16 people

$y=2500$

Step4: Cost per 16 people

$\frac{2500}{16}=156.25$

Step5: Find price difference (16 vs 10)

$156.25 - 130 = 26.25$

Answer:

$\$26.25$