Question

Part 1: Use complete sentences to describe a real-world scenario that could be represented by the inequality 5x + 2y >= 45.
Part 2: Choose one ordered pair that is a solution to the given inequality and explain what that ordered pair means in the context of your real-world scenario.

Answer 1

Let's say that you have a shop that is open for 8 hours a day M-F and 5 hours on Saturday. The shop is open 45 hours.

In the shop they manufacture xylophones and yarrow stick burners. It takes 5 hours to make a xylophone and 2 hours to make a yarrow stick burner. What are the numbers of xylophones and yarrow stick burners that can be made in the shop during a week?

5x + 2y <= 45

For example, if they made 2 xylophones, that would take 10 hours. They could then make up to (45 - 10) / 2 = 35/2 = 17.5 yarrow stick burners. However, maybe demand for yarrow stick burners won't support the sale of 17.5 burners. So they only make 15. Or ten. Or six. That is permitted. However, there isn't enough time to make 20. If you think you can sell 20 yarrow stick burners, that takes 40 hours, and you only have enough time to make 1 xylophone.

(2,15), (2,10), (2, 6), and (1,20) are all valid ordered pairs under this equation.