MA.912.A.3.15Archived Standard

Solve real-world problems involving systems of linear equations and inequalities in two and three variables.

Remarks

Example 1: Each week, you work a total of 20 hours. Some of the 20 hours is spent working at the local bookstore and some spent at the drugstore. You prefer the bookstore and want to work at least 10 more hours at the bookstore relative to the drugstore. Draw a graph to show the possible combinations of hours that you could work.

Example 2: Let x = the amount of liquid (in milliliters) of a product sold by some company. The income (I) that the company makes from sales of the liquid can be represented by the equation I(x)=10.5x and the expenses (E) for the production of the liquid can be represented by the equation E(x)=5.25x+10,000, where I and E are in dollars. What is the minimum amount of the liquid (in milliliters) that the company must sell to reach the break-even point (the point where income in dollars is equal to expenses in dollars)?

Example 3: You need to rent a car to drive from Pensacola to Key West. You will need the car for 7 days. One car rental agency charges $55 per day and $0.06 per mile. Another rental agency charges $65 per day with unlimited mileage. Which rental offer will cost you less? Create a situation where the rental offer in this situation will cost more than the other offer. Explain.