For a child's birthday party, her family perpares goodies bags for the guests. each goodie bag contains 1 notepad, 2 pencils, 1 whistle, 2 cans of silly strings, 3 gummy bear packs, and 1 yo-yo. their current inventory is 30 notepads, 50 pencils, 28 whistles, 45 cans of silly strings, 60 packs of gummy bears and 50 yo-yos.
1) As "goodie bags" are prepared, which item will be used up first ?
2) how many complete goodie bags can be assembled from their current inventory?
3) when the limiting reactant is fully consumed, how much of each of the other items will be left over?
1) To determine which item will be used up first, we need to find the item with the lowest quantity relative to the number required per goodie bag.
The quantities required per goodie bag are:
- 1 notepad
- 2 pencils
- 1 whistle
- 2 cans of silly strings
- 3 packs of gummy bears
- 1 yo-yo
Let's compare the quantities of each item with their current inventories:
- Notepads: 30/1 = 30 goodie bags
- Pencils: 50/2 = 25 goodie bags
- Whistles: 28/1 = 28 goodie bags
- Cans of silly strings: 45/2 = 22.5 goodie bags (we can't have half a goodie bag, so this item will probably run out first)
- Packs of gummy bears: 60/3 = 20 goodie bags
- Yo-yos: 50/1 = 50 goodie bags
Based on this analysis, the item that will be used up first is the cans of silly strings.
2) To determine the number of complete goodie bags that can be assembled from their current inventory, we need to find the item with the lowest quantity in their inventory, as that will ultimately limit the number of complete goodie bags.
Let's consider each item and its required quantity for one goodie bag:
- Notepad: 30 goodie bags
- Pencil: 25 goodie bags
- Whistle: 28 goodie bags
- Cans of silly strings: 22 goodie bags (we can't have half a goodie bag)
- Packs of gummy bears: 20 goodie bags
- Yo-yos: 50 goodie bags
Since the cans of silly strings limit the number of complete goodie bags to 22, that means they will be able to assemble 22 complete goodie bags from their current inventory.
3) When the limiting reactant (cans of silly strings) is fully consumed, we can calculate how much of each of the other items will be left over.
For the items that are not limiting, the amounts remaining will be their original quantities minus the quantity used for the limiting reactant. Let's calculate:
- Notepads: 30 - 1*22 = 8 remaining.
- Pencils: 50 - 2*22 = 6 remaining.
- Whistles: 28 - 1*22 = 6 remaining.
- Packs of gummy bears: 60 - 3*22 = 14 remaining.
- Yo-yos: 50 - 1*22 = 28 remaining.
Therefore, when the cans of silly strings are fully consumed, there will be 8 notepads, 6 pencils, 6 whistles, 14 packs of gummy bears, and 28 yo-yos remaining.
To answer each of the questions, we will go through the inventory of each item and calculate how many goodie bags can be prepared using the available quantity.
1) To determine which item will be used up first, we need to check which item has the lowest quantity relative to the number required for each goodie bag. Let's compare the quantities:
- Notepads: 30 available, 1 needed per bag
- Pencils: 50 available, 2 needed per bag
- Whistles: 28 available, 1 needed per bag
- Silly strings: 45 available, 2 needed per bag
- Gummy bear packs: 60 available, 3 needed per bag
- Yo-yos: 50 available, 1 needed per bag
Comparing the quantities needed per bag to the available quantities, we can see that the limiting item is the whistle since there are only 28 available, and each bag requires 1 whistle. Therefore, the whistle will be used up first.
2) To calculate how many complete goodie bags can be assembled, we need to determine the maximum number of bags we can make for each item. We'll use the limiting item as the reference:
- Notepads: 30 available / 1 needed per bag = 30 bags
- Pencils: 50 available / 2 needed per bag = 25 bags (since pencils come in pairs)
- Whistles: 28 available / 1 needed per bag = 28 bags
- Silly strings: 45 available / 2 needed per bag = 22 bags (since silly strings come in pairs)
- Gummy bear packs: 60 available / 3 needed per bag = 20 bags
- Yo-yos: 50 available / 1 needed per bag = 50 bags
Taking the minimum value from all the calculations above, we can assemble a maximum of 20 complete goodie bags using the current inventory.
3) Finally, to determine how much of each item will be left over when the limiting reactant is fully consumed (in this case, the whistle), we need to calculate the remaining quantity of each item after making the maximum number of goodie bags.
- Notepads: 30 available - (1 needed per bag * 20 bags = 20) = 10 left
- Pencils: 50 available - (2 needed per bag * 20 bags) = 10 left
- Whistles: 28 available - (1 needed per bag * 20 bags) = 8 left
- Silly strings: 45 available - (2 needed per bag * 20 bags) = 5 left
- Gummy bear packs: 60 available - (3 needed per bag * 20 bags) = 0 left (fully consumed)
- Yo-yos: 50 available - (1 needed per bag * 20 bags) = 30 left
After making the maximum number of goodie bags, the inventory will have 10 notepads, 10 pencils, 8 whistles, 5 cans of silly strings, 0 packs of gummy bears (fully consumed), and 30 yo-yos remaining.
I hope this explanation helps! Let me know if you have any further questions.
30 notepads = 30 bags
50 pencils = 25 bags
28 whistles = 28 bags
45 cans silly strinbgs = 22 bags
60 packs gummy bears = 20 bags
50 yo-yos = 50 bags
I'm sure you can complete these problems from here.