Question

oseph set up a lemonade stand in his front yard, where he hopes to make at least $18 in profit. He makes $0.36 profit on every regular cup sold and $0.28 profit on every small cup sold.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of regular cups of lemonade Joseph must sell
y = the number of small cups of lemonade Joseph must sell

Answer 1

To describe the situation using an inequality, we will set up the equation based on the profits from the regular cups and small cups sold.

Let:
- \( x \) = the number of regular cups sold
- \( y \) = the number of small cups sold
- Profit from regular cups = \( 0.36x \)
- Profit from small cups = \( 0.28y \)

Joseph wants to make at least $18 in profit. This can be expressed as:

\[
0.36x + 0.28y \geq 18
\]

Now, to express this inequality in standard form, we need to eliminate the decimals. To do this, we can multiply every term by 100 (to shift the decimals):

\[
100(0.36x) + 100(0.28y) \geq 100(18)
\]

This simplifies to:

\[
36x + 28y \geq 1800
\]

Thus, the inequality in standard form that describes the situation is:

\[
36x + 28y \geq 1800
\]