Question

Shelby has a lemonade stand in her front yard. She has enough supplies to make a maximum of 192 ounces of lemonade. A large cup holds 14 ounces of lemonade and a small cup holds 8 ounces of lemonade. x = number of large cups y = number of small cups Which inequality in standard form represents this situation? A) 14 + x + 8 + y ≥ 192 B) 14 + x + 8 + y ≤ 192 C) 14x + 8y ≥ 192 D) 14x + 8y ≤ 192

Answer 1

Considering the capacity of each cup, the inequality that models the situation is:

D) 14x + 8y ≤ 192

• A large cup holds 14 ounces of lemonade.

• There are x large cups.

• A small cup holds 8 ounces of lemonade.

• There are y small cups.

From the bullet-point, the total amount that can be held is:

$T = 14x + 8y$

She has enough supplies to make a maximum of 192 ounces of lemonade, hence:

$T \leq 192$

$14x + 8y \leq 192$

Hence option D is correct.

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