Lesson: Applications on Systems of Inequalities Mathematics • 9th Grade
In this lesson, we will learn how to solve applications of systems of inequalities by translating each condition into an inequality.
A shepherd wants to build a rectangular sheep barn. The length of the barn must be more than 88 m and its perimeter must be less than 253 m. Derive the system of inequalities that describes the situation, denoting the length of the barn by and its width by .
A carpenter wants to buy two types of nails; the first type costs 6 pounds per kilogram, and the second type costs 9 pounds per kilogram. He needs at least 5 kg of the first type and at least 7 kg of the second. He can spend less than 55 pounds. Using to represent the amount of the first type and to represent the second type, state the system of inequalities that represents this situation.
Charlotte wants to make dresses and suits. Each dress or suit will have the same quantity of cloth and the same number of buttons.
The following inequality represents the number of dresses () and the number of suits () that she can make with 25 m2 of cloth: .
Additionally, the following inequality represents the number of dresses () and the number of suits () that she can make with 100 buttons: .
Given that she has 25 m2 of cloth and 100 buttons, does she have enough cloth to make 2 dresses and 3 suits?