Suppose that a certain municipality uses the equation y=3(x-50)+30 to determine the fine assessed a car which exceeds the 50 mph speed limit. Let x=speed of the car (in mph) and y=corresponding fine in dollars.
a)What is the fine for traveling at 55 mph?
b)If the fine is $126, what is the speed of the car?
c)If car A travels at 60 mph and car B travels at 90 mph, then car B is traveling 50% faster than car A. However the fine for car B is what percent higher than that of car A?
i just really need help with c. i know a is $45 and b is 102 mph but i don't get c
I disagree with your b) answer of 102
3(x-50) + 30 = 126
3(x-50) = 96
x-50 = 32
x = 32+50 = 82 mph
c) fine for A is 3(60-50) + 30 = $60
fine for B is 3(90-50) + 30 = $150
increase in speed = 30 mph
increase in fine = 150-60 = $90
percentage increase = 90/60 = 1.5 or 150% increase in the fine.
yeah, i found out b was wrong after working it out again, but thanks so much for explaining c~
a) To find the fine for traveling at 55 mph, we need to substitute 55 for x in the equation y = 3(x-50) + 30 and solve for y.
Substituting x = 55 into the equation:
y = 3(55-50) + 30
y = 3(5) + 30
y = 15 + 30
y = 45
Therefore, the fine for traveling at 55 mph is $45.
b) To find the speed of the car if the fine is $126, we need to set the equation y = 3(x-50) + 30 equal to 126 and solve for x.
Substituting y = 126 into the equation:
126 = 3(x-50) + 30
126 = 3x - 150 + 30
126 = 3x - 120
Adding 120 to both sides of the equation:
126 + 120 = 3x
246 = 3x
Dividing both sides by 3:
246/3 = x
82 = x
Therefore, the speed of the car is 82 mph if the fine is $126.
c) To determine what percent higher the fine for car B is compared to that of car A, we need to calculate the difference in fines and express it as a percentage of car A's fine.
The fine for car A traveling at 60 mph:
y = 3(60-50) + 30
y = 3(10) + 30
y = 30 + 30
y = 60
The fine for car B traveling at 90 mph:
y = 3(90-50) + 30
y = 3(40) + 30
y = 120 + 30
y = 150
The difference in fines = Fine of car B - Fine of car A:
150 - 60 = 90
To determine the percentage increase, we divide the difference by the fine of car A and multiply by 100:
(90/60) * 100 = 150%
Therefore, the fine for car B traveling at 90 mph is 150% higher than the fine for car A traveling at 60 mph.