Let's Watch
Opening weekend at the Geocove waterpark was a smashing success! Guests had a great time, and the park met its earnings goal.
In the giftshop, Isla sold out of many items. She needs to reorder both sun hats and beach towels. Sun hats cost the gift shop five dollars and fifty cents each, and beach towels cost the gift shop seven dollars each. Isla can spend no more than five hundred dollars to order more sun hats and beach towels.
She has enough space to display and store less than 50 total sun hats and beach towels. Isla wonders how many sun hats and beach towels she can order and stay within her budget, while maximizing her display and storage space.
How can Isla use mathematics to figure this out?
One way is to write a system of linear inequalities. A system of linear inequalities is a set of two or more linear inequalities with the same variables. You have been learning about systems of linear equations. These are sets of two or more linear equations that have the same variables.
You can also create systems of linear inequalities to solve problems like the one Isla is facing. Systems of linear inequalities are frequently used to solve problems in computer science, design, and business.
In this lesson you will learn how to write systems of linear inequalities using either a description or a graph. Then you will be able to help Isla complete her order of sun hats and beach towels for the Geocove waterpark!
Question
Explain why this is a system of linear equations.
\({y = 3 + \frac{1}{2}x}\)
\({y = 2x - 3}\)
This is a system of linear equations because it contains two equations, both of which have the same variables, and the power on the \(x\)-variable is one.
