A standard dorm bedroom at most colleges is 10 ft. wide by 15 ft. long. A bag of regular M&Ms has approximately 200 candies inside of it and usually costs around 67 cents. How much money would it cost to completely fill a dorm bedroom with regular M&Ms? a) Clearly state how you will approach solving this problem. List any assumptions that you would have to make. b) What is your educated guess of how much money it would take to completely fill a dorm bedroom with regular M&Ms? Do this part without any calculations. c) Actually solve the problem using your assumptions from part a) and any calculations that you feel are necessary. Your answer need only be given to one significant figure.
measure the density of a large bag of candies, put themin a measureing cup to get volume, then on a kitchen scale to get mass.
you have mass/cup now, change mass to number of candies, and cups to ft^3
you now have density in number/ft^3
pretty easy from then on
a) To solve this problem, we need to determine the number of regular M&Ms required to fill the dorm bedroom, and then calculate the cost of that quantity of M&Ms.
Assumptions:
1. We will assume that the M&Ms can be stacked in a single layer without any spaces between them.
2. We will assume that the shape of the M&Ms is irrelevant to the calculations.
b) Without any calculations, we can make an educated guess that it would cost quite a lot of money to completely fill a dorm bedroom with regular M&Ms. Given that each bag of M&Ms costs around 67 cents and there are approximately 200 candies in each bag, we can infer that it would take a substantial number of bags to fill a room.
c) To actually solve the problem, we need to calculate the number of M&Ms required to fill the room and then multiply it by the cost per bag.
1. Convert the dimensions of the room to inches: 10 ft x 12 inches = 120 inches (width), 15 ft x 12 inches = 180 inches (length).
2. Calculate the total area of the room: 120 inches x 180 inches = 21,600 square inches.
3. Divide the total area by the area of a single M&M. Since the shape of an M&M is roughly cylindrical, we can estimate its area to be around 0.075 square inches (assuming a diameter of approximately 0.3 inches).
21,600 square inches ÷ 0.075 square inches = 288,000 M&Ms.
4. Calculate the number of bags required: 288,000 M&Ms ÷ 200 M&Ms/bag = 1,440 bags.
5. Multiply the number of bags by the cost per bag: 1,440 bags x $0.67/bag = $964.80.
Therefore, it would cost approximately $964.80 to completely fill a dorm bedroom with regular M&Ms.
a) To solve this problem, we need to determine the volume of the dorm bedroom and then calculate the number of bags of M&Ms required to fill that volume. Finally, we will multiply the number of bags by the cost of each bag to find the total cost.
To find the volume of the bedroom, we will multiply its width by its length. Assumptions we need to make include assuming that the M&Ms perfectly fill all the available space in the room, assuming the bags don't take up any space, and assuming that no M&Ms are lost or wasted during the filling process.
b) Without performing any calculations, we can make an educated guess that it would take a significant amount of money to fill an entire dorm bedroom with M&Ms. Considering that a single bag of M&Ms costs 67 cents and we need to fill a large room, the cost is likely to be quite high.
c) Let's calculate the total cost using the assumptions mentioned above:
First, we calculate the volume of the dorm bedroom:
Volume = width * length = 10 ft * 15 ft = 150 ft^2.
Next, we need to convert the volume from square feet to cubic inches since the volume of each M&M is typically given in cubic inches. We know that 1 ft = 12 inches, so we can convert as follows:
Volume = 150 ft^2 * (12 inches / 1 ft)^2 = 150 * 12^2 cubic inches.
Assuming a bag of M&Ms has approximately 200 candies, we need to find the number of bags required to fill the volume of the room:
Number of bags = Volume / Candies per bag = (150 * 12^2 cubic inches) / (200 candies).
To find the cost of filling the room, we multiply the number of bags by the cost per bag:
Total cost = Number of bags * Cost per bag = (Volume / Candies per bag) * Cost per bag.
Since we are only required to give the answer to one significant figure, we can round the number of bags to the nearest whole number and the total cost to the nearest cent.
Please note that the cost of M&Ms can vary and the number of candies per bag is an estimate, so the actual cost may differ.