Question

For a certain product, the revenue is given by
R = 50x
and the cost is given by
C(x) = 30x + 1200.
To obtain a profit, the revenue must be greater than the cost. For what values of x will there be a profit?

Answer 1

x> ___

Answer 2

We can represent the relationship described as an inequality,
50x > 30x + 1200
Since we know that Revenue (50x) must be greater than Cost (30x + 1200)
We will then use the inequality to solve for x. First, let us subtract 30x from both sides of the equation:
50x - 30x > 30x -30x + 1200
20x > 1200
Then, let us divide both sides of the equation by 20:
20x/20 > 1200/20
x > 60

Based on this result, can you answer the question: "For what values of x will there be a profit?"

Answer 3

ah thank you for the explanation, for some reason i was getting it mixed up and subtracting 50 first so was confused

Answer 4

can you help with 1 similar question?
Thrift rents a compact car for $38 per day, and General rents a similar car for $25 per day plus an initial fee of $91. For how many days d would it be cheaper to rent from General?
d > ___

Answer 5

i got. d>7 but not sure if its right

Answer 6

Sure, this is a similar problem so we could approach it a similar way.
The Thrift car goes for $38 each day, so the cost of renting this car would be (38d), if "d" is the number of days.
The General car goes for $25 each day plus an initial $91, so the cost of renting this car would be (25d + 91)
We want to find the number of days for which it is *cheaper* to rent from General, so we could write the inequality:
Thrift_cost > General_cost
38d > 25d + 91
Similarly to before, we can start by subtracting 25d from both sides:
38d - 25d > 25d - 25d + 91
13d > 91
Then dividing both sides by 13:
13d/13 > 91/13
d > 7
So, it would seem the answer you got is correct, and it would indeed be cheaper to rent the General car for longer than 7 days!

Answer 7

excellent, looks like we got the same steps too. thank you so much!

Answer 8

No problem, glad you figured it out :)