A salesperson has found that the number x of televisions she can sell at a certain price p is related to the equation
x=-1/5p + 90
A) Find the number of TVs she will sell if the price is $375
B) WRite a formula for the revenue when x TVs are sold
C)Find the revenue generated by TV sales if they are priced at $400 each
Can you do any of this? Part A is a matter of substituting $375 for p and solving for x. Just where are you having trouble (and the why would help us help you).
Yes, I can help you with all parts of the question. Let's start with Part A.
To find the number of TVs she will sell if the price is $375, we need to substitute $375 for p in the equation x = -1/5p + 90 and solve for x.
Substituting $375 for p in the equation:
x = -1/5(375) + 90
Now we can simplify and solve the equation:
x = -1/5 * 375 + 90
x = -75 + 90
x = 15
Therefore, the salesperson will sell 15 TVs if the price is $375.
Now, let's move on to Part B.
To write a formula for the revenue when x TVs are sold, we need to consider that the revenue is the product of the number of TVs sold (x) and the price per TV (p). In this case, the price per TV is not explicitly given, but we can use the equation x = -1/5p + 90 to derive it.
R = x * p
Substituting the equation x = -1/5p + 90 into the revenue formula:
R = (-1/5p + 90) * p
Now we can simplify and rewrite the formula:
R = (-1/5)p^2 + 90p
Therefore, the formula for the revenue when x TVs are sold is R = (-1/5)p^2 + 90p.
Finally, let's solve Part C.
To find the revenue generated by TV sales if they are priced at $400 each, we need to substitute $400 for p in the revenue formula R = (-1/5)p^2 + 90p.
Substituting $400 for p in the equation:
R = (-1/5)(400)^2 + 90(400)
Now we can simplify and solve the equation:
R = (-1/5)(160,000) + 36,000
R = -32,000 + 36,000
R = 4,000
Therefore, the revenue generated by TV sales if they are priced at $400 each is $4,000.