Question
Ahmad earned a total of $92 from selling jewelry at a fair. He earned $8 for selling one necklace. He also earned $7 for each bracelet he sold. How many bracelets did he sell?
(a) Write an equation to help answer the question above.
Choose the correct form below and fill in the blanks using only 7,8, and 92.
(The variable x is used to represent the number of bracelets.)
• (?)x + (?) = (?)
• (?)x - (?) = (?)
(b)
Write an expression to help answer the question above
Choose the correct form below and fill in the blanks using only 7, 8, and 92.
• (?)+(?)/(?)
• (?)-(?)/(?)
(c) How many bracelets did Ahmad sell?
(a) Write an equation to help answer the question above.
Choose the correct form below and fill in the blanks using only 7,8, and 92.
(The variable x is used to represent the number of bracelets.)
• (?)x + (?) = (?)
• (?)x - (?) = (?)
(b)
Write an expression to help answer the question above
Choose the correct form below and fill in the blanks using only 7, 8, and 92.
• (?)+(?)/(?)
• (?)-(?)/(?)
(c) How many bracelets did Ahmad sell?
Answers
GPT-4o mini
To solve the problem step-by-step, we'll begin with part (a).
### (a) Writing an equation:
1. Ahmad earned $8 for each necklace he sold. Let’s denote the number of necklaces sold as \( n \). The total earnings from necklaces will then be \( 8n \).
2. Ahmad earned $7 for each bracelet sold, and we denote the number of bracelets sold as \( x \). The total earnings from bracelets will be \( 7x \).
The total earnings from both necklaces and bracelets must equal $92:
\[
8n + 7x = 92
\]
To fill in the blanks according to the provided choices:
• **(?)x + (?) = (?)**
So we can write:
• **(7)x + (0) = (92 - 8n)** (This is the rearrangement)
However, since we don't know how many necklaces were sold, we can't progress further with \( n \).
For simplicity’s sake, let’s assume Ahmad sold a certain number of necklaces, \( n \), to find bracelets \( x \).
If we know he sold 1 necklace, for example:
- 8(1) + 7x = 92 → Here we would have \( 7x + 8 = 92 \).
But we need not complicate. So, let’s just focus on the second format:
• **(?)x - (?) = (?)**
This is not usually a preferred format since we want \( 7x + 8 = 92 \) rather than rearranging it.
Let’s identify clearly:
- Based on what we set up, we can state:
• **(7)x - (0) = (92 - 8n)**
This would also go; unfortunately, we can’t fill all parameters without knowing \( n \).
### (b) Writing an expression:
For the expression to evaluate the total earnings based on sold pieces, we could use:
• **(?)+(?)/(?)**
To set something simpler:
If we denote how many items and their respective earnings correctly, a simpler form is:
- The total earnings from sales could be simplified into one clear expression:
- Earning from necklaces + earnings from bracelets / what earned is 92:
So if we set something lesser:
- Earnings (7x for bracelets and necklaces at some value n)
Perhaps we can lay this, but without defining much about \( n \)...
A clearer expression becomes hard.
But solidly up:
• **(8n) + (7x) / (92)**
Once again, define it via a clearer expression.
### (c) How many bracelets did Ahmad sell?
If we assume a situation where Ahmad only sold necklaces or focused on selling only bracelets, and eventually tests solving:
Assuming he sold \( n \):
Say he sold \( 1 necklace, we assume that was case based 8, then:
1. **8 + 7x = 92**
2. **7x = 92 - 8**
3. **7x = 84**
4. **x = 84 / 7**
5. **x = 12**
So Ahmad sold **12 bracelets** if he sold 1 necklace.
To finalize, if he sold no or around his 12 bracelets strictly without necklaces, earnings simplify down often yields variations could persist, but based systematize we can circle this within the combinations.
Thus:
### Final Answer:
Ahmad sold **12 bracelets** if he sold 1 necklace.
### (a) Writing an equation:
1. Ahmad earned $8 for each necklace he sold. Let’s denote the number of necklaces sold as \( n \). The total earnings from necklaces will then be \( 8n \).
2. Ahmad earned $7 for each bracelet sold, and we denote the number of bracelets sold as \( x \). The total earnings from bracelets will be \( 7x \).
The total earnings from both necklaces and bracelets must equal $92:
\[
8n + 7x = 92
\]
To fill in the blanks according to the provided choices:
• **(?)x + (?) = (?)**
So we can write:
• **(7)x + (0) = (92 - 8n)** (This is the rearrangement)
However, since we don't know how many necklaces were sold, we can't progress further with \( n \).
For simplicity’s sake, let’s assume Ahmad sold a certain number of necklaces, \( n \), to find bracelets \( x \).
If we know he sold 1 necklace, for example:
- 8(1) + 7x = 92 → Here we would have \( 7x + 8 = 92 \).
But we need not complicate. So, let’s just focus on the second format:
• **(?)x - (?) = (?)**
This is not usually a preferred format since we want \( 7x + 8 = 92 \) rather than rearranging it.
Let’s identify clearly:
- Based on what we set up, we can state:
• **(7)x - (0) = (92 - 8n)**
This would also go; unfortunately, we can’t fill all parameters without knowing \( n \).
### (b) Writing an expression:
For the expression to evaluate the total earnings based on sold pieces, we could use:
• **(?)+(?)/(?)**
To set something simpler:
If we denote how many items and their respective earnings correctly, a simpler form is:
- The total earnings from sales could be simplified into one clear expression:
- Earning from necklaces + earnings from bracelets / what earned is 92:
So if we set something lesser:
- Earnings (7x for bracelets and necklaces at some value n)
Perhaps we can lay this, but without defining much about \( n \)...
A clearer expression becomes hard.
But solidly up:
• **(8n) + (7x) / (92)**
Once again, define it via a clearer expression.
### (c) How many bracelets did Ahmad sell?
If we assume a situation where Ahmad only sold necklaces or focused on selling only bracelets, and eventually tests solving:
Assuming he sold \( n \):
Say he sold \( 1 necklace, we assume that was case based 8, then:
1. **8 + 7x = 92**
2. **7x = 92 - 8**
3. **7x = 84**
4. **x = 84 / 7**
5. **x = 12**
So Ahmad sold **12 bracelets** if he sold 1 necklace.
To finalize, if he sold no or around his 12 bracelets strictly without necklaces, earnings simplify down often yields variations could persist, but based systematize we can circle this within the combinations.
Thus:
### Final Answer:
Ahmad sold **12 bracelets** if he sold 1 necklace.