Part A: Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points) Part B: Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation. (4 points)

Part C: Explain how the equations from Part A and Part B differ. (2 points)

Part A: x0.50 + 3 = 18.50

Part B: x0.75 + 3 - x0.10 = 21

Part C: The equations from Part A and Part B differ because of the cost of plastic cup.

Step-by-step explanation:

Let x represent the number of cup of lemonade sold. Therefore, we have:

Part A:

This situation can be represented by the following equation:

x0.50 + 3 = 18.50

Part B:

This situation can be represented by the following equation:

x0.75 + 3 - x0.10 = 21

Part C:

The equations from Part A and Part B differ because of the cost of plastic cup.

For equation from Part A, revenue is the same as profit as Sydney does incur any cost to buy plastic cup before selling her lemonade.

For equation from Part B, revenue is different from profit because Daria has to incur the cost of plastic cup which $0.10 per cup of lemonade before selling her lemonade.

Part A

0.15·x + 3 = 18.50

Part B

0.65·x + 3 - y = 21.00

Part C

The equation in part A gives the total revenue of the yard sale, while the equation in part B gives the profit of the yard sale

Step-by-step explanation:

Part A

The total amount Sydney made selling lemonade = $18.50

The amount she sold a cup of lemonade = $0.50

The amount she received as tip from a neighbor = $3

Let x represent the number of cups sold, we have;

0.15·x + 3 = 18.50

Part B

The profit Daria made = 21.00

The price per cup of lemonade = $0.75

The amount she received as tip = $3

The cost of each plastic cup = $0.10

Let x represent the number of cups sold, we have;

0.75·x - 0.1·x + 3 - y = 21.00

∴ 0.65·x + 3 - y = 21.00

Where;

y = The cost of making the lemonade

Part C

The difference in the two equation is that the first equation relates to total revenue, while the second equation takes account of the costs of the cup and he lemonade

table 3 represents a direct variation function. : )