Question

There are two lemonade stands that sell lemonade called stand A and stand B. The total cost for lemonade at Stand A is $4 (C) plus $2 per ice (I). The total cost for lemonade at Stand B is $8 (C) plus $1 per ice (I). Which Lemonade stand is cheaper.

Answer 1

To compare the costs of lemonade at Stand A and Stand B based on the number of ice cubes (I), we can express the total cost (T) for each stand mathematically.

**Stand A:**
- Total cost \( T_A = 4 + 2I \)

**Stand B:**
- Total cost \( T_B = 8 + 1I \)

To determine which stand is cheaper, let's find the expression for the costs and compare them.

We can set the equations equal to each other to find the break-even point:

\[
4 + 2I = 8 + 1I
\]

Subtract \(1I\) from both sides:

\[
4 + I = 8
\]

Now subtract 4 from both sides:

\[
I = 4
\]

Now we can interpret this solution:
- If you buy **4 ice cubes** or fewer, Stand A is cheaper.
- If you buy **more than 4 ice cubes** (i.e., **5 or more**), Stand B becomes cheaper.

**Summary:**
- For **I ≤ 4**: Stand A is cheaper.
- For **I > 4**: Stand B is cheaper.