Question

during summer vacation, ben decides to sell hot dogs and pretzels on a food cart in manhattan. it costs ben $0.50 for each hot dog and $0.40 for each pretzel. he has only $100 to spend each day on hot dogs and pretzels. he wants to sell at least 200 items each day. if h is the number of hot dogs and p is the number of pretzels, which inequality would be part of a system of inequalities used to determine the total number of hot dogs and pretzels ben can sell? 1. $h + p leq 200$ 2. $h + p geq 200$ 3. $0.50h + 0.40p geq 200$ 4. $0.50h + 0.40p leq 200$

Explanation:

Step1: Identify item count condition

Ben wants to sell at least 200 items total. The total number of items is the sum of hot dogs ($h$) and pretzels ($p$). "At least" translates to the greater than or equal to inequality.
$h + p \geq 200$

Step2: Eliminate incorrect options

• Option 1 uses $\leq$, which would mean selling 200 or fewer items (contradicts the requirement).
• Options 3 and 4 use cost values, but the question refers to the number of items, not the cost budget.

Answer:

1. $h + p \geq 200$