Final answer:
The correct total profit equation for DeAnn's lemonade stand is 2x + 4y - 0.3x - 0.5y - 50 > 200, which accounts for the revenue and costs of selling lemonade and slushies. The correct cost equation is 0.3x + 0.5y + 50 < 90, ensuring that the total costs do not exceed her initial investment capacity. Thus, the correct answer is A.
Step-by-step explanation:
DeAnn is operating a lemonade stand and aims to achieve a profit of more than $200 after paying her costs. When setting up the total profit equation and cost equation, it's important to account for both revenue and expenses. The revenue from the lemonade cups is represented by $2x and from the slushies by $4y. The cost of the supplies for lemonade is $0.30 per cup and for slushies is $0.50 per cup. The cost for the vendor license is a fixed amount of $50.
To create the total profit equation, subtract the cost of supplies and vendor license from the revenue and set this value greater than the desired profit of $200. To create the cost equation, add up the supply costs and the vendor license fee and set this value to be less than the amount DeAnn is willing to spend upfront, which is $90.
The correct equations are:
Total Profit Equation: 2x + 4y - 0.3x - 0.5y - 50 > 200
Cost Equation: 0.3x + 0.5y + 50 < 90
Therefore, the correct answer is A. This will help DeAnn to determine how many cups of lemonade (x) and slushies (y) she needs to sell to exceed her profit goal while staying within her initial budget constraints.