Sergei runs a bakery. He needs at least 175 kilograms of flour in total to complete the holiday orders he's received. He only has 34 kilograms of flour, so he needs to buy more. The flour he likes comes in bags that each contain 23 kilograms of flour. He wants to buy the smallest number of bags possible to get the amount of flour he needs.

Let $ F $ represent the number of bags of flour that Sergei buys. Which inequality describes this scenario?

A. $ 34 + 23F \leq 175 $
B. $ 34 + 23F \geq 175 $
C. $ 23 + 34F \leq 175 $
D. $ 23 + 34F \geq 175 $

The correct inequality that represents Sergei's situation is: "34 + 23F ≤ 175." This equation ensures that the sum of his existing flour (34 kilograms) and the flour he plans to buy in bags (23F) does not exceed the required 175 kilograms.

Explanation:

Sergei needs to buy enough bags of flour (23 kilograms each) to reach a total of at least 175 kilograms. To represent this as an inequality, we need to find the condition where the sum of the flour he already has (34 kilograms) and the flour he buys in bags (23F) is less than or equal to 175 kilograms. This means that option "a. 34+23F≤175" accurately describes the scenario.

In this inequality, 34 represents the flour Sergei already has, 23F represents the flour he intends to buy, and the inequality is set to less than or equal to 175 to ensure he has at least 175 kilograms of flour, making it the correct choice. Mathematical inequalities and their applications in real-world scenarios to solve problems like this.

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