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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.The freshman and sophomore classes at Arcadia High School are decorating floats for homecoming. The freshmen have already spent on their float, plus they need to buy floral sheeting that costs per roll. The sophomores, who have spent so far on theirs, still need to purchase vinyl grass at per roll. Both classes plan to buy the same number of rolls, since they have the same area to cover. By coincidence, the two floats will have the same total cost in the end. How much will each class spend in total? How many rolls will each class be buying?The two classes will have each spend _____ in total by buying _____ rolls.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.The freshman and sophomore classes at Arcadia High School are decorating floats for homecoming. The freshmen have already spent on their float, plus they need to buy floral sheeting that costs per roll. The sophomores, who have spent so far on theirs, still need to purchase vinyl grass at per roll. Both classes plan to buy the same number of rolls, since they have the same area to cover. By coincidence, the two floats will have the same total cost in the end. How much will each class spend in total? How many rolls will each class be buying?The two classes will have each spend _____ in total by buying _____ rolls.
- Define Variables: Let's define the variables.Let be the number of rolls each class will buy.Let be the total amount of money each class will spend.Freshmen's cost equation: Sophomores' cost equation:
- Set Up Equations: Set up the system of equations.Freshmen: Sophomores:
- Substitution to Solve: Use substitution to solve for . Since both 's represent the total cost and they are equal, we can set the equations equal to each other:
- Solve for x: Solve for x.
- Solve for y: Use the value of to solve for . We can use either of the original equations to find . Let's use the freshmen's equation:
- Check Solution: Check the solution with the sophomores' equation.Since the result is the same, our solution is correct.
