Answer :
Sure, let's break this problem down step-by-step.
### Understanding the problem:
Sergei currently has 34 kilograms of flour and needs at least 175 kilograms in total. The flour he intends to buy comes in bags, each containing 23 kilograms. We need to find:
1. The correct inequality that represents this requirement.
2. The smallest number of bags Sergei needs to buy to meet or exceed 175 kilograms of flour in total.
### Step 1: Establish the inequality
Let [tex]\( F \)[/tex] represent the number of bags of flour Sergei buys. Each bag adds 23 kilograms of flour.
So, if Sergei buys [tex]\( F \)[/tex] bags, the total amount of flour he will have is:
[tex]\[ 34 + 23F \][/tex]
This total needs to be at least 175 kilograms, so we set up the inequality:
[tex]\[ 34 + 23F \geq 175 \][/tex]
Therefore, the correct inequality is:
[tex]\[ (B) \, 34 + 23F \geq 175 \][/tex]
### Step 2: Solve the inequality
To find the smallest number of bags, solve the inequality for [tex]\( F \)[/tex]:
[tex]\[ 34 + 23F \geq 175 \][/tex]
Subtract 34 from both sides:
[tex]\[ 23F \geq 141 \][/tex]
Now, divide both sides by 23 to solve for [tex]\( F \)[/tex]:
[tex]\[ F \geq \frac{141}{23} \][/tex]
Calculate the division:
[tex]\[ F \geq 6.13 \][/tex]
Since [tex]\( F \)[/tex] represents the number of bags and must be a whole number, we round up to the next whole number:
[tex]\[ F = 7 \][/tex]
### Conclusion:
The smallest number of bags Sergei can buy to meet his requirement is 7. This means that if he buys 7 bags, he will have enough flour to complete the holiday orders.
So the final answers are:
1. The correct inequality is [tex]\( 34 + 23F \geq 175 \)[/tex].
2. The smallest number of bags Sergei needs to buy is 7.
### Understanding the problem:
Sergei currently has 34 kilograms of flour and needs at least 175 kilograms in total. The flour he intends to buy comes in bags, each containing 23 kilograms. We need to find:
1. The correct inequality that represents this requirement.
2. The smallest number of bags Sergei needs to buy to meet or exceed 175 kilograms of flour in total.
### Step 1: Establish the inequality
Let [tex]\( F \)[/tex] represent the number of bags of flour Sergei buys. Each bag adds 23 kilograms of flour.
So, if Sergei buys [tex]\( F \)[/tex] bags, the total amount of flour he will have is:
[tex]\[ 34 + 23F \][/tex]
This total needs to be at least 175 kilograms, so we set up the inequality:
[tex]\[ 34 + 23F \geq 175 \][/tex]
Therefore, the correct inequality is:
[tex]\[ (B) \, 34 + 23F \geq 175 \][/tex]
### Step 2: Solve the inequality
To find the smallest number of bags, solve the inequality for [tex]\( F \)[/tex]:
[tex]\[ 34 + 23F \geq 175 \][/tex]
Subtract 34 from both sides:
[tex]\[ 23F \geq 141 \][/tex]
Now, divide both sides by 23 to solve for [tex]\( F \)[/tex]:
[tex]\[ F \geq \frac{141}{23} \][/tex]
Calculate the division:
[tex]\[ F \geq 6.13 \][/tex]
Since [tex]\( F \)[/tex] represents the number of bags and must be a whole number, we round up to the next whole number:
[tex]\[ F = 7 \][/tex]
### Conclusion:
The smallest number of bags Sergei can buy to meet his requirement is 7. This means that if he buys 7 bags, he will have enough flour to complete the holiday orders.
So the final answers are:
1. The correct inequality is [tex]\( 34 + 23F \geq 175 \)[/tex].
2. The smallest number of bags Sergei needs to buy is 7.
