Answer:
- $0.75×200 + $1.25×g ≥ $250
- g ≥ 80
Explanation:
Writing the Inequality
You are expected to understand that the revenue from selling tickets to 200 sophomores is 200×$0.75, and the revenue from selling tickets to g guests is $1.25×g.
You are also expected to interpret the problem setup as requring that the total of the revenue from these ticket sales is desired to be at least $250. That is, ...
... 200×$0.75 + $1.25×g ≥ $250
This is the inequality you are being asked to write (or one like it).
Generally, you will see this without the dollar signs. I put them there to remind what the units are that go with the numbers, and to make sure that the units of the equation are consistent, (A number times dollars is still dollars. Adding dollars, I should only get dollars.)
Solution
You solve this inequality the same way you solve any 2-step equation: subtract the constant that is on the side with the variable, then divide by the coefficient of the variable. (No additional steps are necessary because the divisor is positive.)
... 1.25g ≥ 250 -200×.75
,,, 1.25g ≥ 100
... g ≥ 100/1.25
... g ≥ 80