Constraint Systems Worksheets Grade 9

1. Mason has a budget of $272 to buy two types of plants: ferns that cost $17 each and succulents that cost $12 each. He needs at least 7 ferns and at least 12 succulents. Write the system of inequalities that represents this situation, using x for ferns and y for succulents.
2. A right triangle is drawn on a coordinate plane with vertices at A(0,0), B(9,0), and C(0,12). A circle is circumscribed around this triangle such that all three vertices lie on the circle's circumference. What is the area of this circumscribed circle? (Use π = 3.14)
3. Lena is designing a rectangular garden with a perimeter of 40 meters. She wants the length to be at least 3 meters more than the width, and the area must be at least 60 square meters. Write a system of inequalities that represents the constraints on the garden's dimensions, using l for length and w for width.

…and 4 more problems

1. A rectangular garden has a length that is 3 meters more than twice its width. The area of the garden must be at least 54 square meters, and the perimeter cannot exceed 30 meters. Write a system of inequalities that represents these constraints, using w for width and l for length.
2. Ava is organizing a school fundraiser and can spend at most $180 on prizes. She wants to buy at least 15 prizes total, with no more than 8 of the expensive prizes that cost $12 each and at least 10 of the budget prizes that cost $7 each. Write a system of inequalities that represents these constraints, where x represents the number of expensive prizes and y represents the number of budget prizes.
3. A tech company is analyzing the profitability of their new software product. The revenue function is R(x) = -0.5x² + 60x, where x is the price per license in dollars. The cost function is C(x) = 20x + 800. The company wants the profit to be at least $1,000, and they cannot charge more than $80 per license due to market constraints. Write a system of inequalities that represents these business constraints.

…and 3 more problems

1. Aisha is designing a rectangular stage for a school play. The stage must have a perimeter of at least 50 meters but no more than 70 meters. Additionally, the area of the stage must be at least 150 square meters. If the length is 5 meters more than twice the width, write a system of inequalities that represents all possible dimensions for Aisha's stage, using w for width and l for length.
2. Aroha is organizing a school event with a budget of $320. She needs to buy chairs that cost $18 each and tables that cost $25 each. She must have at least 12 chairs and at least 8 tables, and the total number of items must be at least 25. Write the system of inequalities that represents these constraints, where x is the number of chairs and y is the number of tables.
3. Matiu is buying school supplies with a budget of $85. He needs at least 15 notebooks and pens combined. Notebooks cost $4 each and pens cost $2 each. He needs at least twice as many pens as notebooks. Write the system of inequalities representing these constraints.

…and 3 more problems