Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.The freshman and sophomore classes at Georgetown High School are decorating floats for homecoming. The freshmen have already spent $264 on their float, plus they need to buy floral sheeting that costs $29 per roll. The sophomores, who have spent $241 so far on theirs, still need to purchase vinyl grass at $30 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?

Answer 1

1) Let's begin by writing down the equations we need.

Freshmen

y=264+29x Note that $29 depends on the number of rolls

Sophomore

y= 241+30x

2) Now that we know the equations that describe those expenses, let's apply the Substitution Method

Let's plug into the 1st equation the value of y.