The freshman and sophomore classes at Hillsdale High School are decorating floats for homecoming. The freshmen have already spent $55 on their float, plus they need to buy floral sheeting that costs $46 per roll. The sophomores, who have spent $255 so far on theirs, still need to purchase vinyl grass at $42 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?
Let's assume both classes will buy "x" rolls of floral sheeting and vinyl grass each.
So, the total cost for the freshmen class would be $55 + $46x.
And the total cost for the sophomore class would be $255 + $42x.
According to the problem, both classes will have the same total cost.
So, $55 + $46x = $255 + $42x.
By rearranging the equation, we get $46x - $42x = $255 - $55.
Simplifying further, we have $4x = $200.
Dividing both sides of the equation by 4, we find x = $200 / 4 = $50.
Therefore, both classes will be buying 50 rolls each.
The total cost for the freshmen class would be $55 + $46 * 50 = $55 + $2300 = $2355.
And the total cost for the sophomore class would be $255 + $42 * 50 = $255 + $2100 = $2355.
Thus, each class will be spending a total of $2355.