1. A car company has found that there is a linear relationship between the amoun
ID: 3097300 • Letter: 1
Question
1. A car company has found that there is a linear relationship between the amount of money it spends on advertising and the number of cars it sells. When it spent 60,000 dollars on advertising, it sold 440 cars. Moreover, for each additional 10,000 dollars spent, they sell 40 more cars.A. If a car company invested 90,000 dollars in advertising, then how many cars did it sell?
B. If a car company sold 800 cars, then how much did it invest in advertising?
C. Write an equation in y=mx +b form for the number of cars sold as a function of the amount of money spent on advertising. Give units and real world meaning for m and b.
D. Write an equation in y=mx + b form for the amount of money spent on advertising as a function of the number of cars sold. Give units and real world meaning for m and b.
Explanation / Answer
C) y = number of cars sold, x = amount of money spend on advertising Slope = m = (40 number of cars sold) /(10000 money spend on advertising) = 0.004(cars/1$) (Given in the problem) y-intercept: y = mx + b 440 = 0.004(60000)+b (pick any point and substitute the numbers, picked ($60000, 440cars)440 = 240 + b (Multiply)
b = 200 (Subtract both sides 240 and simplify)
Your function: y = 0.004x + 200 D) y = amount of money spend on advertising, x = number of cars sold Slope = m = $10000/(40 cars) = $250/car (Given in the problem)
y-intercept: y = mx + b 60000 = 250(440) + b (Substitute any point, I substituted (440 cars, $60000)
60000 = 110000 + b (Multiply)
b = -50000 (Subtract from both sides 110000 and simplify)
Your equation: y = 250x - 50000
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