High School

Felipe is selling cups of lemonade at a stand outside his house. He has enough supplies on hand to make a maximum of 182 ounces of lemonade. A regular cup holds 11 ounces of lemonade, and a small cup holds 4 ounces of lemonade.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables:

- [tex]x[/tex] = the number of regular cups of lemonade
- [tex]y[/tex] = the number of small cups of lemonade

A. [tex]11x + 4y \leq 182[/tex]
B. [tex]4x - 11y \leq 182[/tex]
C. [tex]11x - 4y \leq 182[/tex]
D. [tex]4x + 11y \leq 182[/tex]

Answer :

To solve the problem and find the inequality that describes the situation, let's go through the steps together:

1. Understand the Variables and Quantities:
- Felipe can make a maximum of 182 ounces of lemonade.
- A regular cup holds 11 ounces.
- A small cup holds 4 ounces.
- We define:
- [tex]\( x \)[/tex] as the number of regular cups.
- [tex]\( y \)[/tex] as the number of small cups.

2. Set Up the Inequality:
- The total ounces of lemonade used is the sum of the ounces in regular cups and small cups.
- The total lemonade used by regular cups is [tex]\( 11x \)[/tex] (since each regular cup uses 11 ounces).
- The total lemonade used by small cups is [tex]\( 4y \)[/tex] (since each small cup uses 4 ounces).

3. Formulate the Inequality:
- The inequality should show that the total number of ounces used (by both regular and small cups) is no more than 182 ounces.
- Thus, the equation will be:
[tex]\( 11x + 4y \leq 182 \)[/tex].

This inequality represents the condition Felipe must meet while selling lemonade, where the total ounces of lemonade in all cups must not exceed 182 ounces.