To say is at least 50, you would write:
To say at most 50 you would write:
The monthly revenue achieved by selling x boxes of candy is figured to be
x(5 - 0.05x) dollars. The wholesale cost of each box of candy is $1.50. How many boxes must be sold each month to achieve a profit of at least $60?
What about if the question asked:
How many boxes must be sold each month to achieve a profit of at most $60?
In terms of inequality word problems, what is the difference between at least and at most questions?
Thanks
Profit is revenue-costs, so in this case:
p=x(5-0.05x) - 1.5x=-0.05 x^2 + 3.5 x
we want this to be at least 60 dollars, so we want p>=60.
Now as p is a quadratic in x, with a negative coefficient to the x^2 term
p>=60 between the roots of:
p=-0.05x^2+3.5x =60
or between the roots of 0.05 x^2-3.5 x +60=0.
The roots of this quadratic are 30 and 40, so the profit >=$60, for
30<=x<=40.
RonL