Question

The freshman and sophomore classes at Oak Grove High School are decorating floats for homecoming. The freshmen have already spent $450 on their float, plus they need to buy floral sheeting that costs $23 per roll. The sophomores, who have spent $452 so far on theirs, still need to purchase vinyl grass at $22 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 many rolls will each class be buying? How much will each class spend in total?

Answer 1

Let 'x' be the number of rolls each class will be buying.
The total cost for the freshmen's float is $450 + $23x.
The total cost for the sophomores' float is $452 + $22x.
Since the two floats will have the same total cost:
$450 + $23x = $452 + $22x
Subtracting $22x from both sides, we get:
$23x - $22x = $452 - $450
$1x = $2
Therefore, each class will be buying 2 rolls.
The total cost for each class is:
For the freshmen: $450 + $23 * 2 = $450 + $46 = $496.
For the sophomores: $452 + $22 * 2 = $452 + $44 = $496.
Thus, each class will spend $496 in total. Answer: \boxed{2}.