Infinite Solutions Worksheets Grade 8

1. Liam is designing a rectangular garden with a perimeter of 48 feet. The length of the garden is 4 feet more than twice its width. Write an equation to represent this situation and find the dimensions of the garden.
2. Isabella is volunteering at a local animal shelter. She is tasked with organizing the donation of dog food bags. The shelter received a donation of 12 bags of dry dog food and 18 cans of wet dog food. Isabella wants to create identical care packages for the dogs, each containing the same number of bags of dry food and the same number of cans of wet food, using all the donated food. She claims that if she makes 6 care packages, the equation 12x + 18 = 6(2x + 3) describes the situation, where x represents the number of bags of dry food per package. How many solutions does this equation have, and what does that tell you about Isabella's plan?
3. Mere is helping her aunt set up chairs for a school concert. They need to arrange chairs in rows with the same number of chairs in each row. Mere notices that if they set up 4 chairs in each row, they will have 6 chairs left over. If they set up 6 chairs in each row, they will have 2 chairs left over. Mere writes the equation 4x + 6 = 6x + 2, where x represents the number of rows. Does this equation have one solution, no solution, or infinitely many solutions? Explain your reasoning.

…and 3 more problems

1. A chemist is preparing a solution and needs to determine when two different mixing processes will create the same concentration. The concentration after x minutes is given by the equation 4(3x - 7) + 12 = kx - 16. For what value of k will this equation have infinitely many solutions, representing identical concentration at all times?
2. A school is planning a field trip and needs to rent buses. Each bus can hold 40 students. The total cost for renting buses is $500 plus $25 per bus. If the total cost for the trip is $900, how many buses did the school rent?
3. Emma is planning a school fundraiser selling bracelets and keychains. She has $120 to spend on materials. Bracelet materials cost $2 per bracelet, and keychain materials cost $3 per keychain. If Emma wants to make the same number of each item and spend all her money, how many of each item should she make?

…and 4 more problems

1. A rectangle is drawn on a coordinate plane with vertices at (2, 1), (8, 1), (8, 5), and (2, 5). A line passes through the midpoints of the top and bottom sides of this rectangle. What is the equation of this line?
2. Emma is volunteering at a community garden where they are planting flower beds. The garden coordinator tells her that the number of marigold plants in one bed, when multiplied by 5 and then increased by 7, is equal to 7 more than 5 times the number of marigold plants. How many marigold plants are in the bed, and what does this tell you about the number of solutions to the equation representing this situation?
3. Sophia is helping her aunt set up a lemonade stand. They use a recipe that calls for a certain number of lemons. The recipe says: 'The number of lemons needed, when multiplied by 6 and then increased by 11, is equal to 6 times the number of lemons plus 11.' How many solutions does this equation have for the number of lemons needed?

…and 5 more problems