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. What is the expression needed to find his total profit? What was his total profit?

Question

GPT-4o mini · Answer

To find Juan's total profit from the lemonade stand, we first need to define a few key variables based on the information provided:

Profit for Day 1: This is given as $12. So, the profit for Day 1 is $12.
Daily Revenue and Expenses for Days 2 to 4: We will need values for his earnings (revenue) and costs (expenses) for each of these days in order to calculate the additional profits.

Let’s say that the profits for Days 2, 3, and 4 are calculated as follows:

Let's say he earned $E_2$, $E_3$, and $E_4$ on Days 2, 3, and 4 respectively.
Let’s also say his expenses for Day 2, Day 3, and Day 4 are $C_2$, $C_3$, and $C_4$ respectively.

The profit for each of these days can be expressed as:

Profit for Day 2: $P_2 = E_2 - C_2$
Profit for Day 3: $P_3 = E_3 - C_3$
Profit for Day 4: $P_4 = E_4 - C_4$

The total profit can then be computed as:

\[ \text{Total Profit} = P_1 + P_2 + P_3 + P_4 \]

Substituting $P_1$, $P_2$, $P_3$, and $P_4$:

\[ \text{Total Profit} = 12 + (E_2 - C_2) + (E_3 - C_3) + (E_4 - C_4) \]

Thus, the expression to find his total profit is:

\[ \text{Total Profit} = 12 + E_2 + E_3 + E_4 - (C_2 + C_3 + C_4) \]

To find the actual total profit, you will just need the values for his earnings and costs from Days 2 to 4. For example, if he earned $15, $20, and $25 on those days and spent $5, $10, and $15 respectively, you could calculate it as follows:

Earnings: $15 + 20 + 25 = 60$
Costs: $5 + 10 + 15 = 30$

Then, substituting these values into the profit equation:

\[ \text{Total Profit} = 12 + 60 - 30 = 42 \]

So, once you have the values for $E_2$, $E_3$, $E_4$, $C_2$, $C_3$, and $C_4$, plug them into the expression to find Juan's total profit.