Need some help on a word problem. It has a storage chest. The dimensions for the top of the chest are 28 in wide, 46 in long, and 1 in high. The bottom of the chest is 28 in wide, 46 in long, and 17 in high. The word problem is Cynthia packs the chest with sweater bags that are 12 inches wide, 13 inches long, and 2 inches high. How many sweater bags can Cynthia fit in the chest. I don't know how to go about solving this problem. If you could explain the steps to me I would really appreciate it so I will know how to do it on future problems like this one. Thanks.
To solve this word problem, we need to find the number of sweater bags that can fit into the given storage chest. Here are the steps you can follow:
Step 1: Calculate the volume of the chest:
- The top of the chest has dimensions 28 in by 46 in by 1 in. So, its volume is: 28 in * 46 in * 1 in = 1288 cubic inches.
- The bottom of the chest has dimensions 28 in by 46 in by 17 in. So, its volume is: 28 in * 46 in * 17 in = 21224 cubic inches.
- To find the actual volume of the chest, we need to consider the difference between the top and bottom volumes, which gives us: 21224 cubic inches - 1288 cubic inches = 19936 cubic inches.
Step 2: Calculate the volume of each sweater bag:
- The sweater bags have dimensions 12 in by 13 in by 2 in. So, the volume of each bag is: 12 in * 13 in * 2 in = 312 cubic inches.
Step 3: Divide the volume of the chest by the volume of each sweater bag:
- 19936 cubic inches (chest volume) / 312 cubic inches (sweater bag volume) = approximately 63.87.
Step 4: Round the result down to the nearest whole number:
- Since we can't have a fraction of a sweater bag, we round down to 63.
Thus, Cynthia can fit 63 sweater bags in the chest.