Question

1. a lemonade stand sells lemonade and sweet tea. on a hot afternoon, the stand sold 20 total items. a sweet tea costs $3, and a lemonade cost $5. the total sales revenue was $76. how many lemonades and how many sweet teas were sold? use any method to solve and show your work.

Explanation:

Step1: Define variables

Let \( x \) be the number of lemonades sold and \( y \) be the number of sweet teas sold.
We know two equations:

1. The total number of items sold: \( x + y = 20 \) (so \( y = 20 - x \))
2. The total revenue: \( 5x + 3y = 76 \)

Step2: Substitute \( y \) into revenue equation

Substitute \( y = 20 - x \) into \( 5x + 3y = 76 \):
\( 5x + 3(20 - x) = 76 \)
Expand: \( 5x + 60 - 3x = 76 \)
Simplify: \( 2x + 60 = 76 \)

Step3: Solve for \( x \)

Subtract 60 from both sides: \( 2x = 76 - 60 = 16 \)
Divide by 2: \( x = \frac{16}{2} = 8 \)

Step4: Solve for \( y \)

Use \( y = 20 - x \), so \( y = 20 - 8 = 12 \)

Answer:

8 lemonades and 12 sweet teas were sold.