Question

The freshman and sophomore classes at Danville High School are decorating floats for homecoming. The freshmen have already spent $500 on their float, plus they need to buy floral sheeting that costs $25 per roll. The sophomores, who have spent $200 so far on theirs, still need to purchase vinyl grass at $100 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?Write a system of equations, graph them, and type the solution.

Answer 1

Let x represent the number of rolls of either of the floral sheeting or vinyl grass that they need to buy.

The freshmen have already spent $500 on their float, plus they need to buy floral sheeting that costs $25 per roll. This means that the cost of buying x rolls of floral sheeting is 25 * x = 25x. The total cost of their float would be

500 + 25x

The sophomores, who have spent $200 so far on theirs, still need to purchase vinyl grass at $100 per roll. The cost of purchasing x rolls of vinyl grass is

100 * x = 100x. The total cost of their float is

200 + 100x

Let the cost of each float be y. If the two floats will have the same total cost in the end, the system of equations would be

y = 500 + 25x

y = 200 + 100x

To graph the equations, we would substitute values of x into each equation and find the corresponding values of y. These would be plotted on the graph.

For y = 500 + 25x,

if x = 1, y = 500 + 25(1) = 500 + 25 = 525

if x = 2, y = 500 + 25(2) = 500 + 50 = 550

if x = 3, y = 500 + 25(3) = 500 + 75 = 575

For y = 200 + 100x,

if x = 1, y = 200 + 100(1) = 200 + 100 = 300

if x = 2, y = 200 + 100(2) = 200 + 200 = 400

if x = 3, y = 200 + 100(3) = 200 + 300 = 500

The graph is shown below

The green line represents y = 25x + 500

The purple line represents y = 100x + 200

The solution is the x and y coordinates of the point where both lines intersect. The solution is

(4, 600)