Question
Select ALL the correct answers.
Shania is making eight gift bags to give out to her friends coming over to her house for a movie night. Each gift bag will contain x nail polishes and a manicure kit. Including tax, each nail polish costs $2.50 and each manicure kit costs $4.00.
The following expression shows the amount of money Shania will spend on gift bags.
Which of the following descriptions are equivalent ways to write this problem?
8(2.5x+4)
Shania will spend x dollars each on 20 nail polishes and 4 dollars each on eight manicure kits.
Shania will spend 6.5x dollars on each of the eight gift bags, for a total of 52x dollars.
Shania will spend a total of 20x dollars on nail polish and a total of 32 dollars on manicure kits.
Shania will spend 2.5 dollars each on x nail polishes for eight gift bags and 4 dollars each on eight manicure kits.
Shania is making eight gift bags to give out to her friends coming over to her house for a movie night. Each gift bag will contain x nail polishes and a manicure kit. Including tax, each nail polish costs $2.50 and each manicure kit costs $4.00.
The following expression shows the amount of money Shania will spend on gift bags.
Which of the following descriptions are equivalent ways to write this problem?
8(2.5x+4)
Shania will spend x dollars each on 20 nail polishes and 4 dollars each on eight manicure kits.
Shania will spend 6.5x dollars on each of the eight gift bags, for a total of 52x dollars.
Shania will spend a total of 20x dollars on nail polish and a total of 32 dollars on manicure kits.
Shania will spend 2.5 dollars each on x nail polishes for eight gift bags and 4 dollars each on eight manicure kits.
Answers
GPT-4o mini
To analyze the different descriptions in relation to the expression \(8(2.5x + 4)\), we need to break down what this expression represents.
- **8** represents the total number of gift bags.
- **\(2.5x\)** represents the total cost of \(x\) nail polishes in each gift bag, where each nail polish costs $2.50.
- **4** represents the total cost of one manicure kit for each gift bag, where each manicure kit costs $4.00.
Now we can examine each description:
1. **8(2.5x + 4)**: This is simply the original expression for the total cost. It represents spending on both nail polish and manicure kits across all gift bags.
2. **Shania will spend x dollars each on 20 nail polishes and 4 dollars each on eight manicure kits.**: This is incorrect since it suggests \(x\) dollars for 20 nail polishes, but each nail polish specifically costs $2.50. There should be \(2.5x\) instead.
3. **Shania will spend 6.5x dollars on each of the eight gift bags, for a total of 52x dollars.**: Incorrect. Each gift bag actually costs \(2.5x + 4\), and it does not equate to \(6.5x\) per bag.
4. **Shania will spend a total of 20x dollars on nail polish and a total of 32 dollars on manicure kits.**: This is correct. The total for nail polish when summing across all bags would be \(20x\) (since there are \(8\) gift bags each with \(x\) nail polishes, leading to \(8*x*2.5 = 20x\)). The total for the manicure kits would be \(8 * 4 = 32\).
5. **Shania will spend 2.5 dollars each on x nail polishes for eight gift bags and 4 dollars each on eight manicure kits.**: This is also correct. It describes how Shania spends for \(x\) nail polishes across \(8\) bags (making it \(8 * 2.5x\)) and \(4\) dollars for each of the \(8\) manicure kits.
The correct responses are:
- **Shania will spend a total of 20x dollars on nail polish and a total of 32 dollars on manicure kits.**
- **Shania will spend 2.5 dollars each on x nail polishes for eight gift bags and 4 dollars each on eight manicure kits.**
- **8** represents the total number of gift bags.
- **\(2.5x\)** represents the total cost of \(x\) nail polishes in each gift bag, where each nail polish costs $2.50.
- **4** represents the total cost of one manicure kit for each gift bag, where each manicure kit costs $4.00.
Now we can examine each description:
1. **8(2.5x + 4)**: This is simply the original expression for the total cost. It represents spending on both nail polish and manicure kits across all gift bags.
2. **Shania will spend x dollars each on 20 nail polishes and 4 dollars each on eight manicure kits.**: This is incorrect since it suggests \(x\) dollars for 20 nail polishes, but each nail polish specifically costs $2.50. There should be \(2.5x\) instead.
3. **Shania will spend 6.5x dollars on each of the eight gift bags, for a total of 52x dollars.**: Incorrect. Each gift bag actually costs \(2.5x + 4\), and it does not equate to \(6.5x\) per bag.
4. **Shania will spend a total of 20x dollars on nail polish and a total of 32 dollars on manicure kits.**: This is correct. The total for nail polish when summing across all bags would be \(20x\) (since there are \(8\) gift bags each with \(x\) nail polishes, leading to \(8*x*2.5 = 20x\)). The total for the manicure kits would be \(8 * 4 = 32\).
5. **Shania will spend 2.5 dollars each on x nail polishes for eight gift bags and 4 dollars each on eight manicure kits.**: This is also correct. It describes how Shania spends for \(x\) nail polishes across \(8\) bags (making it \(8 * 2.5x\)) and \(4\) dollars for each of the \(8\) manicure kits.
The correct responses are:
- **Shania will spend a total of 20x dollars on nail polish and a total of 32 dollars on manicure kits.**
- **Shania will spend 2.5 dollars each on x nail polishes for eight gift bags and 4 dollars each on eight manicure kits.**