SOLUTION: A car's value depreciates as it accumulates miles. Use the tables below to determine the rate of depreciation for Car 1 and Car 2. After how many miles do the cars have the same va

Question 1132077: A car's value depreciates as it accumulates miles. Use the tables below to determine the rate of depreciation for Car 1 and Car 2. After how many miles do the cars have the same value?
A table of 'Car 1' showing data of Miles and Value as (25000,$22960), (50000,$19680), (75000,$16400)?and (100000,$13120) respectively.
A table of 'Car 2' showing data of Miles and Value as (25000,$20376), (50000,$17806), (75000,$15236)? and (100000,$12666) respectively.
A. The cars will have the same value at 1,160,000 miles.
B. The cars will have the same value at 116,000 miles.
C. The cars will have the same value at 11,600 miles.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
examination of the point pairs for each car yields the following:

the value for car 1 is depreciating by 3280 dollars every 25000 miles.
the value for car 2 is depreciating by 2570 dollars every 25000 miles.

the change in the value of y divided by the change in the value of x for car 1 is therefore equal to -3280 / 25000 = -.1312.

the change in the value of y divided by the change in the value of x for car 2 is therefore equal to -2570 / 25000 = -.1028.

y is the value of the car.
x is the number of miles the car has been driven

the equation for the value of each car is y = mx + b
m is the slope which is the change in the value of y divided by the change in the value of x.
b is the y-intercept.

the equation for car 1 becomes y = -.1312 * x + 26240

the equation for car 2 becomes y = -.1028 * x + 22946

i'm assuming you know how to derive the value of the y-intercept so i won't get into it here.

the cars will have the same value when the equation for car 1 is equal to the equation for car 2.

this occurs when -.1312 * x + 26240 = -.2018 * x + 22946

solve for x in this equation to get x = 3294 /.0284 = 115985.9155.

round this to nearest 1000 to get x = 116000.

that's selection B.

a graph of both equations and their intersection is shown below:

$$$

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