Question

Tre' wants to make at least $200 at his lemonade stand. He sell half cups for 25 cents and full cups for

50 cents. He can sell no more than 250 cups of each. Write a system of inequalities that can be used
to identify the possible combinations of half and full cups to be sold to meet his goal.

Answer 1

Let x represent the number of half cups sold and y represent the number of full cups sold. To meet Tre's goal of making at least $200, we can set up the following system of inequalities:

1. Revenue from half cups: 0.25x
2. Revenue from full cups: 0.50y

Since Tre wants to make at least $200, we can express this as the first inequality:

3. 0.25x + 0.50y ≥ 200

Additionally, Tre can sell no more than 250 cups of each type, so we have the following two inequalities to represent that:

4. x ≤ 250 (limit on half cups)
5. y ≤ 250 (limit on full cups)

These inequalities together form the system of inequalities that can be used to identify the possible combinations of half and full cups to be sold to meet Tre's goal while staying within the cup limits:

0.25x + 0.50y ≥ 200
x ≤ 250
y ≤ 250

Answer 2

To represent the possible combinations of half and full cups that Tre' can sell to meet his goal of making at least $200, you can set up a system of inequalities based on the number of cups and their prices. Let's denote:

x = number of half cups sold
y = number of full cups sold

Now, we can set up the inequalities:

1. Revenue from half cups: 0.25x (since each half cup is sold for 25 cents).
2. Revenue from full cups: 0.50y (since each full cup is sold for 50 cents).

Tre' wants to make at least $200, so the total revenue should be greater than or equal to $200:

0.25x + 0.50y ≥ 200

Additionally, he cannot sell more than 250 cups of each type, so you need to add the following constraints:

3. Number of half cups sold (x) should be less than or equal to 250:

x ≤ 250

4. Number of full cups sold (y) should be less than or equal to 250:

y ≤ 250

So, the system of inequalities to identify possible combinations of half and full cups to meet Tre's goal is:

0.25x + 0.50y ≥ 200
x ≤ 250
y ≤ 250

These inequalities represent the conditions for Tre' to achieve his goal while respecting the limits on the number of cups he can sell.