Create Equations Worksheets Grade 9

1. Emma is building a rectangular garden in her backyard. The garden is divided into two sections: one for vegetables and one for flowers. The vegetable section is a square with side length x meters. The flower section is a rectangle with width y meters and length that is 5 meters longer than the vegetable section's side length. The total area of the garden is 70 square meters. Write an equation in two variables that represents the total area of the garden.
2. Aisha is analyzing the growth of bacteria in a lab experiment. The bacteria population follows the exponential model P(t) = 500 * e^(0.03t), where t is time in hours. She needs to determine when the population will reach 1000 bacteria. Which equation should she solve to find this time?
3. The sum of two numbers is 24. When the larger number is squared and then decreased by the square of the smaller number, the result is 96. What is the larger number?

…and 4 more problems

1. Kaia is designing a small vegetable garden. She wants to create a rectangular plot where the length is 9 meters more than twice the width. The total perimeter of the garden is to be 84 meters. Write an equation in two variables to represent the relationship between the length L and the width W, and then determine the dimensions of the garden.
2. Kaia is organizing a fundraising concert. She rents a venue that costs a fixed fee of $450. Additionally, she needs to pay for security guards, where each guard costs $85, and for sound equipment, which costs a flat rate of $220 plus $15 per hour of use. Write an equation in two or more variables that represents the total cost C of the event in terms of the number of security guards g and the number of hours h the sound equipment is used.
3. Olivia is planning a school fundraiser where she will sell two types of tickets: adult tickets at $15 each and student tickets at $10 each. She needs to raise a total of $2,500. Let x represent the number of adult tickets sold and y represent the number of student tickets sold. Write an equation in two variables that models the total revenue from ticket sales. If she sells 120 adult tickets, how many student tickets must she sell to reach her goal?

…and 3 more problems

1. Emma is designing a rectangular banner for a school event. The banner has a length that is 5 meters more than twice its width. Write an equation that relates the length (L) and width (W) of the banner.
2. Olivia is designing a rectangular garden with a perimeter of 50 meters. If the length is 5 meters more than twice the width, write an equation in two variables that represents this situation.
3. Noah is designing a rectangular mural for a school project. The length of the mural is 6 feet longer than its width. The total area of the mural is 216 square feet. Write an equation in two variables to represent the relationship between the width (w) and the length (l) of the mural, and then write a second equation that relates the area to the width and length. Use these equations to find the dimensions of the mural.

…and 5 more problems