Asked by SS
Sylvia spends $50 at the craft show on candles and ornaments. The candles cost $5 each, and the ornaments cost $7 each. Sylvia buys a total of 8 items at the craft show.
Let x=
number of candles and y=
number of ornaments. Which of the following statements is true?
(1 point)
Responses
The inequality that represents the constraint on the number of candles is x≤8
and on the number of ornaments is y≤8
because the candles and ornaments together cannot be more than 8 items.
The inequality that represents the constraint on the number of candles is x is less than or equal to 8 and on the number of ornaments is y is less than or equal to 8 because the candles and ornaments together cannot be more than 8 items.
The inequality that represents the constraint on the number of candles is x>0
and on the number of ornaments is y>0
because there must be a positive number of candles or ornaments.
The inequality that represents the constraint on the number of candles is x is greater than 0 and on the number of ornaments is y is greater than 0 because there must be a positive number of candles or ornaments.
The inequality that represents the constraint on the number of candles is x≥0
and on the number of ornaments is y≥0
because there cannot be a negative number of candles or ornaments.
The inequality that represents the constraint on the number of candles is x is greater than or equal to 0 and on the number of ornaments is y is greater than or equal to 0 because there cannot be a negative number of candles or ornaments.
The inequality that represents the constraint on number of candles is 0≤x≤8
and on the number of ornaments is 0≤y≤8
because there cannot be a negative number of candles or ornaments and the candles and ornaments together cannot be more than 8 items.
Let x=
number of candles and y=
number of ornaments. Which of the following statements is true?
(1 point)
Responses
The inequality that represents the constraint on the number of candles is x≤8
and on the number of ornaments is y≤8
because the candles and ornaments together cannot be more than 8 items.
The inequality that represents the constraint on the number of candles is x is less than or equal to 8 and on the number of ornaments is y is less than or equal to 8 because the candles and ornaments together cannot be more than 8 items.
The inequality that represents the constraint on the number of candles is x>0
and on the number of ornaments is y>0
because there must be a positive number of candles or ornaments.
The inequality that represents the constraint on the number of candles is x is greater than 0 and on the number of ornaments is y is greater than 0 because there must be a positive number of candles or ornaments.
The inequality that represents the constraint on the number of candles is x≥0
and on the number of ornaments is y≥0
because there cannot be a negative number of candles or ornaments.
The inequality that represents the constraint on the number of candles is x is greater than or equal to 0 and on the number of ornaments is y is greater than or equal to 0 because there cannot be a negative number of candles or ornaments.
The inequality that represents the constraint on number of candles is 0≤x≤8
and on the number of ornaments is 0≤y≤8
because there cannot be a negative number of candles or ornaments and the candles and ornaments together cannot be more than 8 items.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which statement is true regarding the number of candles (x) and ornaments (y) that Sylvia bought, we consider the constraints based on the information provided:
1. Sylvia spent a total of $50 on candles and ornaments.
2. The cost of candles is $5 each, and the cost of ornaments is $7 each.
3. The total number of items (candles and ornaments) she bought is 8.
From this information, we can identify the following constraints:
- **Total cost constraint**:
\[
5x + 7y \leq 50
\]
- **Total items constraint**:
\[
x + y = 8
\]
- **Non-negativity constraint**:
\[
x \geq 0 \quad \text{and} \quad y \geq 0
\]
- **Item upper limit constraint**: Since she bought a total of 8 items, it follows that:
\[
x \leq 8 \quad \text{and} \quad y \leq 8
\]
Considering the options provided:
1. "The inequality that represents the constraint on the number of candles is \( x \leq 8 \) and on the number of ornaments is \( y \leq 8 \) because the candles and ornaments together cannot be more than 8 items." - **True**
2. "The inequality that represents the constraint on the number of candles is \( x \) is less than or equal to 8 and on the number of ornaments is \( y \) is less than or equal to 8 because the candles and ornaments together cannot be more than 8 items." - **Also True**, but the format is slightly different.
3. "The inequality that represents the constraint on the number of candles is \( x > 0 \) and on the number of ornaments is \( y > 0 \) because there must be a positive number of candles or ornaments." - **False**, as she could buy zero of either.
4. "The inequality that represents the constraint on the number of candles is \( x \) is greater than 0 and on the number of ornaments is \( y \) is greater than 0 because there must be a positive number of candles or ornaments." - **False**, similar reasoning.
5. "The inequality that represents the constraint on the number of candles is \( x \geq 0 \) and on the number of ornaments is \( y \geq 0 \) because there cannot be a negative number of candles or ornaments." - **True**.
6. "The inequality that represents the constraint on number of candles is \( 0 \leq x \leq 8 \) and on the number of ornaments is \( 0 \leq y \leq 8 \) because there cannot be a negative number of candles or ornaments and the candles and ornaments together cannot be more than 8 items." - **True**.
Given that we need to select which of the statements is true:
The best conclusion is the last option, which encompasses the entire constraints clearly:
**"The inequality that represents the constraint on number of candles is \( 0 \leq x \leq 8 \) and on the number of ornaments is \( 0 \leq y \leq 8 \) because there cannot be a negative number of candles or ornaments and the candles and ornaments together cannot be more than 8 items."**
1. Sylvia spent a total of $50 on candles and ornaments.
2. The cost of candles is $5 each, and the cost of ornaments is $7 each.
3. The total number of items (candles and ornaments) she bought is 8.
From this information, we can identify the following constraints:
- **Total cost constraint**:
\[
5x + 7y \leq 50
\]
- **Total items constraint**:
\[
x + y = 8
\]
- **Non-negativity constraint**:
\[
x \geq 0 \quad \text{and} \quad y \geq 0
\]
- **Item upper limit constraint**: Since she bought a total of 8 items, it follows that:
\[
x \leq 8 \quad \text{and} \quad y \leq 8
\]
Considering the options provided:
1. "The inequality that represents the constraint on the number of candles is \( x \leq 8 \) and on the number of ornaments is \( y \leq 8 \) because the candles and ornaments together cannot be more than 8 items." - **True**
2. "The inequality that represents the constraint on the number of candles is \( x \) is less than or equal to 8 and on the number of ornaments is \( y \) is less than or equal to 8 because the candles and ornaments together cannot be more than 8 items." - **Also True**, but the format is slightly different.
3. "The inequality that represents the constraint on the number of candles is \( x > 0 \) and on the number of ornaments is \( y > 0 \) because there must be a positive number of candles or ornaments." - **False**, as she could buy zero of either.
4. "The inequality that represents the constraint on the number of candles is \( x \) is greater than 0 and on the number of ornaments is \( y \) is greater than 0 because there must be a positive number of candles or ornaments." - **False**, similar reasoning.
5. "The inequality that represents the constraint on the number of candles is \( x \geq 0 \) and on the number of ornaments is \( y \geq 0 \) because there cannot be a negative number of candles or ornaments." - **True**.
6. "The inequality that represents the constraint on number of candles is \( 0 \leq x \leq 8 \) and on the number of ornaments is \( 0 \leq y \leq 8 \) because there cannot be a negative number of candles or ornaments and the candles and ornaments together cannot be more than 8 items." - **True**.
Given that we need to select which of the statements is true:
The best conclusion is the last option, which encompasses the entire constraints clearly:
**"The inequality that represents the constraint on number of candles is \( 0 \leq x \leq 8 \) and on the number of ornaments is \( 0 \leq y \leq 8 \) because there cannot be a negative number of candles or ornaments and the candles and ornaments together cannot be more than 8 items."**
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