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Answer: 285, choice A</h3>
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Explanation:
x = number of attendees
y = cost
If you increase the number of attendees (x) by 15, then the cost (y) goes up by 105. We see this by subtracting the values
30 - 15 = 15
495 - 390 = 105
Divide the change in cost over the change in people. So we have 105/15 = 7
The 7 represents the unit rate, which is the amount of money it costs for one person. Each time we add a person, it costs $7. So we can say "it costs 7 dollars per person"
At 7 dollars per person, 15 people will be charged 15*7 = 105. However, the table shows $390 is the actual cost. So 390 - 105 = 285 is the base cost
Or you can use the second column. If we had 30 people, then 7*30 = 210 is the cost without the base cost added on. The table shows 495, so 495-210 = 285 which is the same answer as before.
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Alternative method
This method involves more equations and algebra
First use the slope formula. You can use any two points from the table. I'm going to use (15, 390) and (30, 495)
m = slope
m = (y2-y1)/(x2-x1)
m = (495-390)/(30-15)
m = (105)/(15)
m = 7 <<--- this is the unit rate, aka cost per person
Use the slope and one of the points to find the y intercept
y = mx+b
y = 7x+b
390 = 7(15)+b
390 = 105+b
105+b = 390
b = 390-105
b = 285 <<-- this is the y intercept, aka base cost
The base cost is the price you pay to get in the door. This cost stays the same no matter how many people are in your party. The equation would be y = 7x+285. Note how plugging in x = 15 leads to y = 390. At the same time, plugging in x = 30 leads to y = 495.
and second you divide 7 by g(x) to obtain 7 / [√(8x+10) ].