The Webster family is planning a barbecue for one hundred people. The Webster family needs one plastic plate for each person at the barbecue. The Stop and Shop store and Market Place Store both sell plastic plates in packages of fifteen for five dollars and forty-eight cents per package. How many packages of plastic plates does the Webster family need to buy?
Packages of plastic plates are on sale for one-half off regular price at the Stop and Shop store.Packages of plastic plates are on sale for buy one, get one free at the Market Place store. Which store is offering the better buy for plastic plates?
The Market Place store will sell certain items in bulk. If you buy the plates in cartons of four packages of plates,the store will discount the full carton $2.00. You may only buy full cartons.They will not split cartons for this extra savings. Would buying this way save the family money at the sale price? Show all your mathematical thinking.
To find out how many packages of plastic plates the Webster family needs to buy, we need to divide the number of people attending the barbecue by the number of people each package of plastic plates serves.
The Webster family needs 1 plastic plate per person, and each package contains 15 plates. So, the number of packages required can be calculated as follows:
Number of packages = (Number of people) / (Number of people per package)
Number of packages = 100 / 15
Number of packages = 6.6667
Since we cannot buy a fraction of a package, we need to round up to the nearest whole number. Therefore, the Webster family needs to buy 7 packages of plastic plates.
Now let's compare the price and offers at the two stores:
At Stop and Shop, the plastic plates are sold in packages of 15 for $5.48. Since the packages are on sale for half the regular price, the original price of a package would be $5.48 * 2 = $10.96.
At Market Place, the plastic plates are sold in packages of 15, and the offer is buy one, get one free. This means that for every package purchased, one package is given for free. Therefore, the effective price per package is $5.48 / 2 = $2.74.
Now let's calculate the total cost at each store for buying 7 packages of plastic plates:
At Stop and Shop:
Total cost = (Number of packages) * (Price per package)
Total cost = 7 * $10.96
Total cost = $76.72
At Market Place:
Total cost = (Number of packages) * (Price per package)
Total cost = 7 * $2.74
Total cost = $19.18
Therefore, the Market Place store is offering the better buy for plastic plates, as it costs significantly less compared to Stop and Shop.
Now let's consider the bulk purchase option at the Market Place store. If we buy plates in cartons of four packages, the price of each carton will be reduced by $2.00.
Let's calculate the total cost of buying the plates in this way:
Number of full cartons = (Number of packages) / (Number of packages per carton)
Number of full cartons = 7 / 4
Number of full cartons = 1.75
Since we can only buy full cartons, we need to round up to the nearest whole number. Therefore, the Webster family needs to buy 2 full cartons of plates.
Total cost of 2 full cartons = (Number of full cartons) * (Price per carton)
Total cost of 2 full cartons = 2 * ($2.74 * 4 - $2.00)
Total cost of 2 full cartons = 2 * ($9.96 - $2.00)
Total cost of 2 full cartons = 2 * $7.96
Total cost of 2 full cartons = $15.92
By buying the plates in cartons of four packages, the Webster family can save money at the sale price. The total cost of buying 2 full cartons is $15.92, which is less than the cost of buying 7 individual packages ($19.18).
To determine how many packages of plastic plates the Webster family needs to buy, we need to divide the total number of people at the barbecue (100) by the number of plates in each package (15).
Number of packages needed = Total number of people / Number of plates in each package
Number of packages needed = 100 / 15
Using simple division, we find that the Webster family needs to buy approximately 6.67 packages. Since we cannot buy a fraction of a package, we usually round up to ensure we have enough plates. Therefore, the family needs to buy 7 packages of plastic plates.
To compare the offers at the Stop and Shop store and the Market Place store, let's calculate the price per package at each store.
At the Stop and Shop store, a package of plastic plates costs $5.48, and they are on sale for one-half off regular price. Therefore, the sale price per package at the Stop and Shop store is:
Sale price per package = $5.48 / 2 = $2.74
At the Market Place store, the plastic plates are on sale for buy one, get one free. This means that when you buy one package, you get another package for free. So, the price per package at the Market Place store is:
Price per package = $5.48 / 2 = $2.74
Comparing the prices at both stores, we can see that they are the same. Both stores offer the same price per package, which is $2.74.
Now, let's consider the bulk purchasing option at the Market Place store. If we buy plates in cartons of four packages, the store will discount the full carton by $2.00. We need to determine if this bulk purchasing option will save the family money compared to buying individual packages at the sale price.
The original price of a carton of four packages is:
Original price = $5.48 * 4 = $21.92
The discounted price of a carton of four packages is:
Discounted price = $21.92 - $2.00 = $19.92
To determine if buying in cartons will save money, we compare the discounted price of the carton with the price of buying individual packages at the sale price.
Price of individual packages (sale price) = $2.74
Total cost of buying 7 packages individually (at the sale price) = $2.74 * 7 = $19.18
Comparing the total cost of buying individual packages with the discounted price of the carton, we can see that buying in cartons does not save the family money. The total cost of buying individual packages is $19.18, which is less than the discounted price of the carton ($19.92). Therefore, buying in cartons would not save the family money at the sale price.
In conclusion, both stores offer the same price per package for plastic plates. However, buying in cartons at the Market Place store does not save the family money compared to buying individual packages at the sale price. Therefore, the better buy for plastic plates would be to purchase them individually at the sale price from either store.
100 / 15 = 6.67 = 7 packages
7 * 5.48 = 38.36 regular price
7 (5.48 / 2) = 19.18 at Stop and Shop
4 * 5.48 = 21.92 at Market Place
I'll leave it to you to figure the last problem.