Three students are participating in a walkathon. The data for each student is shown.
Student A: The equation y = 14x represents the amount of money raised (y) for walking (x) miles.
Student B: $42 is raised after walking 3 miles.
Student C:
Miles Walked 6 9
Money Raised $72 $108
Determine which student raised the least amount of money after walking 8 miles.
Student A
Student B
Student C
All three students raised the same amount of money after walking 8 miles.
To determine which student raised the least amount of money after walking 8 miles, we need to find the amount of money each student raised after walking 8 miles.
For Student A, we can use the equation y = 14x, where x represents the number of miles walked. Plugging in x = 8, we get y = 14(8) = 112. So, Student A raised $112 after walking 8 miles.
For Student B, we know that $42 is raised after walking 3 miles. We can set up a proportion to find how much is raised after walking 8 miles:
(42 dollars / 3 miles) = (x dollars / 8 miles)
Cross multiplying, we get 3x = 336, and solving for x, we find that x = 112. So, Student B also raised $112 after walking 8 miles.
For Student C, we can look at the given data points. When the miles walked is 6, the money raised is $72, and when the miles walked is 9, the money raised is $108. We can use these two points to find the equation for Student C's money raised:
Using the formula for the equation of a line (y = mx + b), we can determine the slope (m) and y-intercept (b):
m = (change in y)/(change in x) = (108 - 72) / (9 - 6) = 36 / 3 = 12
Using the slope-intercept form of a line (y = mx + b), we can substitute one of the known points into the equation to solve for the y-intercept:
72 = 12(6) + b
72 = 72 + b
b = 0
So the equation for Student C's money raised is y = 12x.
Plugging in x = 8, we get y = 12(8) = 96. So, Student C raised $96 after walking 8 miles.
Comparing the amounts raised, we see that Student C raised the least amount of money after walking 8 miles with $96. Therefore, the answer is Student C.