Question

1A. Nayeli wants to earn some extra money so she sells lemonade for $2 per cup and orange juice for $3 per cup. She sells a total of 100 cups and earns $240. Later she wants to find the number of cups of lemonade and the number of cups of orange juice she sold. Which system of equations below represents this situation?

1. 2x + 3y = 240 AND x + y = 100
2. 2x + 3y = 100 AND x + y = 240
3. x + 2y = 100 AND 3x + y = 240
4. 2x + 100 = 240.AND x = 3y


1B. In the context of the problem, what does your solution (x,y) mean? Fill in the blanks for the solution sentence below: Nayeli sold ____ cups of lemonade and ____ cups of orange juice. Write your answer in this form: 20, 40

Answer 1

1. 2x + 3y = 240 AND x + y = 100

Nayeli sold 60 cups of lemonade and 40 cups of orange juice.

Explanation:

Let

Number of cups of lemonade sold = x

Number of cups of orange juice sold = y

The system of equation could be represented by:

2x + 3y = 240 (1)

x + y = 100 (2)

from (2)

x = 100 - y

Substitute into (1)

2x + 3y = 240 (1)

2(100 - y) + 3y = 240

200 - 2y + 3y = 240

- 2y + 3y = 240 - 200

y = 40 cups

Substitute y = 40 into (2)

x + y = 100 (2)

x + 40 = 100

x = 100 - 40

x = 60 cups

Nayeli sold 60 cups of lemonade and 40 cups of orange juice.

(x, y) = (60, 40)