Infinite Solutions Worksheets Grade 8

1. A local bakery sells cupcakes and cookies. For a school event, Liam bought 3 cupcakes and 2 cookies for a total of $9.50. Emma bought 1 cupcake and 4 cookies from the same bakery for $8.50. If the price of a cupcake is represented by 'c' and the price of a cookie is represented by 'k', which system of equations represents this situation?
2. A school is organizing a field trip to the science museum. The total cost for the trip is $800, which includes a $200 booking fee plus $15 per student. The school wants to know how many students need to attend for the total cost per student to be exactly $20. Write and solve an equation to find the number of students.
3. A local bakery sells cupcakes for $2.50 each and cookies for $1.25 each. Noah bought some cupcakes and cookies for a school event and spent $23.75 total. The number of cookies he bought was 3 more than twice the number of cupcakes. How many cupcakes did Noah buy?

…and 4 more problems

1. 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?
2. Emma is helping her cousin with a lemonade stand. They decide to charge $3 for each cup of lemonade. Emma's cousin claims that the amount of money they earn, in dollars, can be found using the equation 3x + 5 = 3(x + 2) - 1, where x is the number of cups sold. Emma thinks this equation will always give the correct total, no matter how many cups they sell. Is Emma's cousin correct? Does the equation have one solution, no solution, or infinitely many solutions? Explain your reasoning.
3. A triangle is drawn on a coordinate plane with vertices at A(2, 3), B(8, 3), and C(5, 7). A line is drawn from vertex C to the midpoint of side AB. What are the coordinates of this midpoint?

…and 3 more problems

1. A line is drawn on a coordinate plane that passes through the points (8, 14) and (12, 20). Another line is drawn that passes through the points (10, 17) and (14, 23). These two lines are graphed on the same coordinate plane. How many solutions (intersection points) do the equations representing these two lines have?
2. A triangle is drawn on a coordinate plane with vertices at A(1, 2), B(5, 2), and C(3, 6). A line is drawn from point A to the midpoint of side BC. What are the coordinates of this midpoint?
3. 4(3x - 2) + 8 = 12x = ?

…and 4 more problems