Create Systems Worksheets Grade 9

1. Liam is managing a small business that produces handmade crafts. He finds that his weekly profit P (in dollars) can be modeled by the quadratic function P(x) = -2x² + 80x - 600, where x represents the number of crafts sold. His friend Emma suggests that a linear model P(x) = 20x - 200 might be more accurate for their current production scale. At what production levels do these two profit models predict the same profit, and what is that profit amount?
2. Emma is selling two types of lemonade at her stand. Small cups sell for $1.50 and large cups sell for $2.50. On Saturday, she sold 35 cups total and collected $67.50. Write a system of equations to represent this situation, using s for small cups and l for large cups.
3. A rectangular garden is drawn on a coordinate plane with vertices at (2, 1), (8, 1), (8, 5), and (2, 5). A diagonal path is drawn from (2, 1) to (8, 5), and a circular fountain is centered at the intersection point of this diagonal with another line segment from (2, 5) to (8, 1). Find the coordinates of the fountain's center by solving the system of equations formed by these two diagonals.

…and 4 more problems

1. Matiu is analyzing two different investment plans for his savings. Plan A offers a fixed annual return of $120 plus 4% simple interest on the principal amount invested. Plan B offers a fixed annual return of $80 plus 6% simple interest on the same principal amount. Matiu wants to know what principal amount would make both plans yield the same total annual return, and what that total annual return would be. Write a system of equations to represent this situation and solve for the principal amount and the total annual return.
2. A scientist is studying bacterial growth in two different cultures. Culture A starts with 200 bacteria and doubles every 3 hours. Culture B starts with 50 bacteria and grows according to the function B(t) = 50 × 4^(t/4), where t is time in hours. After how many hours will both cultures contain the same number of bacteria?
3. A right triangle is drawn on a coordinate plane with vertices at A(0,0), B(6,0), and C(0,8). A circle is inscribed in this triangle, tangent to all three sides. Find the area of this inscribed circle.

…and 3 more problems

1. Charlotte is selling two types of handmade candles. She sold 9 large candles and 13 small candles for a total of $287. A large candle costs $8 more than a small candle. Write a system of equations to represent this situation, using L for the price of a large candle and S for the price of a small candle.
2. Noah is selling two types of handmade candles. He sold 9 large candles and 8 small candles for a total of $287. A large candle costs $7 more than a small candle. Write a system of equations to represent this situation, using L for the price of a large candle and S for the price of a small candle.
3. Mason is analyzing a rectangular garden on a coordinate grid. The garden's length is 7 meters more than twice its width. The perimeter of the garden is 62 meters. Write a system of two equations to represent this situation, where L represents the length and W represents the width. Do not solve the system.

…and 4 more problems