SOLUTION: When a company spends no money on advertising, it sells 300 units. But for each additional $5000 spent, an additional 20 units are sold. Question: If x is the amount of money th

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Question 263200: When a company spends no money on advertising, it sells 300 units. But for each additional $5000 spent, an additional 20 units are sold.
Question: If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x.
Thank you!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"When a company spends no money on advertising, it sells 300 units" means that When x=0, then y=300 giving us the point (0,300)

"But for each additional $5000 spent, an additional 20 units are sold" adds 5000 to x=0 to get x=5000 and adds 20 to y=300 to get y=320. So we have another point (5000,320)


Now let's assume that we're dealing with a linear equation (ie a straight line). We only need to points to find the equation of this line. So let's find the equation of the line that goes through the points (0,300) and (5000,320)


First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=0 and y%5B1%5D=300.
Also, is the second point . So this means that x%5B2%5D=5000 and y%5B2%5D=320.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28320-300%29%2F%285000-0%29 Plug in y%5B2%5D=320, y%5B1%5D=300, x%5B2%5D=5000, and x%5B1%5D=0


m=%2820%29%2F%285000-0%29 Subtract 300 from 320 to get 20


m=%2820%29%2F%285000%29 Subtract 0 from 5000 to get 5000


m=1%2F250 Reduce


So the slope of the line that goes through the points and is m=1%2F250


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-300=%281%2F250%29%28x-0%29 Plug in m=1%2F250, x%5B1%5D=0, and y%5B1%5D=300


y-300=%281%2F250%29x%2B%281%2F250%29%280%29 Distribute


y-300=%281%2F250%29x%2B0 Multiply


y=%281%2F250%29x%2B0%2B300 Add 300 to both sides.


y=%281%2F250%29x%2B300 Combine like terms.


y=%281%2F250%29x%2B300 Simplify


So the equation that goes through the points and is y=%281%2F250%29x%2B300


Note: your book might want everything in decimal form. Since 1%2F250=0.004, this means that the equation is also y=0.004x%2B300