Question
Juan ran the lemonade stand for 3 more days after his first day profit of $12. Each day, he
used the money from sales to purchase more lemons, cups, and sugar to make more
lemonade. The table shows how much he spent and earned each day.
Day 2
Day 3
Day 4
Spent
7
12
9
Earned
16
ZZ
18
What is the expression needed to find his total profit?
What was his total profit?
used the money from sales to purchase more lemons, cups, and sugar to make more
lemonade. The table shows how much he spent and earned each day.
Day 2
Day 3
Day 4
Spent
7
12
9
Earned
16
ZZ
18
What is the expression needed to find his total profit?
What was his total profit?
Answers
GPT-4o mini
To find the total profit Juan made from running his lemonade stand over the 4 days, we need to consider both his spending and earnings for each day.
First, let's define total profit over multiple days:
Total Profit = Total Earnings - Total Spent
**Given Data:**
1. Day 1:
- Profit = $12 (not given explicitly in terms of spending vs earnings, but we can infer that this is the earnings minus spending for Day 1)
2. Day 2:
- Spent = $7
- Earned = $16
- Profit = Earnings - Spending= $16 - $7 = $9
3. Day 3:
- Spent = $12
- Earned = ZZ (we don't know this yet)
- We need to solve for ZZ later.
4. Day 4:
- Spent = $9
- Earned = $18
- Profit = Earnings - Spending = $18 - $9 = $9
Next, we can calculate the total spent and total earned, specifying that ZZ represents the earnings on Day 3.
**Calculating Total Spent:**
- Total spent = Day 1 spend + Day 2 spend + Day 3 spend + Day 4 spend
Assuming Day 1 spent amount is represented by (Earned - Profit in Day 1), we do not have this specific value. Therefore, let's represent it as \( E_1 \).
\[
\text{Total Spent} = E_1 + 7 + 12 + 9
\]
\[
\text{Total Spent} = E_1 + 28
\]
**Calculating Total Earned:**
- Total earned = Day 1 earnings + Day 2 earnings + Day 3 earnings + Day 4 earnings
\[
\text{Total Earned} = 12 + 16 + ZZ + 18
\]
\[
\text{Total Earned} = 46 + ZZ
\]
**Final Profit Expression:**
Now we put these together in the profit expression:
\[
\text{Total Profit} = \text{Total Earned} - \text{Total Spent}
\]
\[
\text{Total Profit} = (46 + ZZ) - (E_1 + 28)
\]
\[
\text{Total Profit} = 46 + ZZ - E_1 - 28
\]
\[
\text{Total Profit} = 18 + ZZ - E_1
\]
To find a numerical total profit, we need the value of \( ZZ \) (the earnings on Day 3) and the spending on Day 1 (\( E_1 \)).
Since we don't have those exact values in the data, if you find out the value of \( ZZ \) or \( E_1 \), substitute them back to find the total profit.
Assuming we were guessing or knew ZZ (Day 3 earnings), we can simplify:
If we presume that Day 3's earnings also had to yield a profit to keep consistency (let's say he earned 12 dollar profit similar to other days), we could guess and say something along the lines of \( ZZ = 15 \) (let's say) giving us a total approximate profit.
If we give ZZ the value of \( 15 \):
- Then the Total, \( \Rightarrow \) $9 profit on Day 3, assuming same profit pattern.
Finally substituting the values would provide clarity on the numbers.
So:
Profit Total would end as expressed containing variance.
Without exact values for Day 1 and ZZ, the possible profit is dependent on those values.
First, let's define total profit over multiple days:
Total Profit = Total Earnings - Total Spent
**Given Data:**
1. Day 1:
- Profit = $12 (not given explicitly in terms of spending vs earnings, but we can infer that this is the earnings minus spending for Day 1)
2. Day 2:
- Spent = $7
- Earned = $16
- Profit = Earnings - Spending= $16 - $7 = $9
3. Day 3:
- Spent = $12
- Earned = ZZ (we don't know this yet)
- We need to solve for ZZ later.
4. Day 4:
- Spent = $9
- Earned = $18
- Profit = Earnings - Spending = $18 - $9 = $9
Next, we can calculate the total spent and total earned, specifying that ZZ represents the earnings on Day 3.
**Calculating Total Spent:**
- Total spent = Day 1 spend + Day 2 spend + Day 3 spend + Day 4 spend
Assuming Day 1 spent amount is represented by (Earned - Profit in Day 1), we do not have this specific value. Therefore, let's represent it as \( E_1 \).
\[
\text{Total Spent} = E_1 + 7 + 12 + 9
\]
\[
\text{Total Spent} = E_1 + 28
\]
**Calculating Total Earned:**
- Total earned = Day 1 earnings + Day 2 earnings + Day 3 earnings + Day 4 earnings
\[
\text{Total Earned} = 12 + 16 + ZZ + 18
\]
\[
\text{Total Earned} = 46 + ZZ
\]
**Final Profit Expression:**
Now we put these together in the profit expression:
\[
\text{Total Profit} = \text{Total Earned} - \text{Total Spent}
\]
\[
\text{Total Profit} = (46 + ZZ) - (E_1 + 28)
\]
\[
\text{Total Profit} = 46 + ZZ - E_1 - 28
\]
\[
\text{Total Profit} = 18 + ZZ - E_1
\]
To find a numerical total profit, we need the value of \( ZZ \) (the earnings on Day 3) and the spending on Day 1 (\( E_1 \)).
Since we don't have those exact values in the data, if you find out the value of \( ZZ \) or \( E_1 \), substitute them back to find the total profit.
Assuming we were guessing or knew ZZ (Day 3 earnings), we can simplify:
If we presume that Day 3's earnings also had to yield a profit to keep consistency (let's say he earned 12 dollar profit similar to other days), we could guess and say something along the lines of \( ZZ = 15 \) (let's say) giving us a total approximate profit.
If we give ZZ the value of \( 15 \):
- Then the Total, \( \Rightarrow \) $9 profit on Day 3, assuming same profit pattern.
Finally substituting the values would provide clarity on the numbers.
So:
Profit Total would end as expressed containing variance.
Without exact values for Day 1 and ZZ, the possible profit is dependent on those values.