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.

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

What is the smallest number of bags that Sergei can buy to get the amount of flour he needs?

To find the smallest number of bags that Sergei can buy to get the amount of flour he needs, we can set up an inequality. The inequality that represents the problem is 34 + 23F ≤ 175. By solving the inequality, we find that Sergei should buy 7 bags of flour to get the amount he needs.

Explanation:

To find the smallest number of bags that Sergei can buy to get the amount of flour he needs, we can set up an inequality. Let F represent the number of bags of flour that Sergei buys. The inequality that represents the problem is 34 + 23F ≤ 175. This inequality states that the sum of 34 (the amount of flour Sergei already has) and the product of 23 and F (the number of bags he buys) must be less than or equal to 175. To solve for F, we can subtract 34 from both sides of the inequality and then divide both sides by 23. This will give us the smallest whole number value of F.

To subtract 34 from both sides of the inequality, we have: 34 + 23F - 34 ≤ 175 - 34, which simplifies to: 23F ≤ 141.

Then, to isolate F, we divide both sides of the inequality by 23, resulting in: F ≤ 6.13. Since F represents the number of bags, we round up to the nearest whole number. Therefore, Sergei should buy 7 bags of flour to get the amount he needs.

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