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?

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}.

Answer 2

Let's solve this problem step-by-step:

Step 1: Calculate the cost of floral sheeting for the freshmen float.
The cost of floral sheeting per roll is $23.
Let's assume they will buy 'x' rolls.
So, the cost of floral sheeting for the freshmen float is 23x dollars.

Step 2: Calculate the total cost of the freshmen float.
The freshmen have already spent $450 on their float.
So, the total cost of the freshmen float is 450 + 23x dollars.

Step 3: Calculate the cost of vinyl grass for the sophomore float.
The cost of vinyl grass per roll is $22.
Since both classes plan to buy the same number of rolls, the sophomores will also buy 'x' rolls.
So, the cost of vinyl grass for the sophomore float is 22x dollars.

Step 4: Calculate the total cost of the sophomore float.
The sophomores have already spent $452 on their float.
So, the total cost of the sophomore float is 452 + 22x dollars.

Step 5: Set up an equation based on the given information.
Since the two floats will have the same total cost, we can set up an equation:
450 + 23x = 452 + 22x

Step 6: Solve the equation.
450 + 23x = 452 + 22x
23x - 22x = 452 - 450
x = 2

Step 7: Calculate the number of rolls each class will be buying.
Since x = 2, each class will be buying 2 rolls.

Step 8: Calculate the total cost for each class.
For freshmen:
Total cost = 450 + 23x
Total cost = 450 + 23(2)
Total cost = 450 + 46
Total cost = $496

For sophomores:
Total cost = 452 + 22x
Total cost = 452 + 22(2)
Total cost = 452 + 44
Total cost = $496

So, each class will be buying 2 rolls, and each class will spend a total of $496.