Answer :
Sure, I can help with that!
The problem requires us to find the greatest number of 110-kilogram crates, represented by [tex]\( c \)[/tex], that can be added to the shipping container without exceeding its weight limit.
Here's how you can determine this:
1. Understand the total weight capacity: The shipping container has a weight capacity of 23,000 kilograms.
2. Account for already loaded weight: The container already has shipments weighing 3,800 kilograms.
3. Calculate remaining capacity: Subtract the weight of the other shipments from the total capacity to find out how much weight you can still add:
[tex]\[
\text{Remaining weight capacity} = 23,000 - 3,800 = 19,200 \text{ kilograms}
\][/tex]
4. Determine crate weight: Each crate weighs 110 kilograms.
5. Set up the inequality: To find the greatest number of crates [tex]\( c \)[/tex], you want the total weight of these crates plus the already loaded shipments to remain within the 23,000-kilogram limit:
[tex]\[
3,800 + 110c \leq 23,000
\][/tex]
6. Solve the inequality: Subtract 3,800 from 23,000 to find out how much weight can be dedicated to the crates:
[tex]\[
110c \leq 19,200
\][/tex]
Now, divide both sides by 110 to solve for [tex]\( c \)[/tex]:
[tex]\[
c \leq \frac{19,200}{110}
\][/tex]
Performing the division gives:
[tex]\[
c \leq 174.5454\ldots
\][/tex]
7. Determine the greatest whole number: Since [tex]\( c \)[/tex] must be a whole number, we need the largest integer value that satisfies the inequality:
[tex]\[
c \leq 174
\][/tex]
Therefore, the greatest number of 110-kilogram crates that can be loaded into the shipping container is 174. The correct inequality to express this situation is [tex]\( 23,000 \geq 3,800 + 110c \)[/tex].
The problem requires us to find the greatest number of 110-kilogram crates, represented by [tex]\( c \)[/tex], that can be added to the shipping container without exceeding its weight limit.
Here's how you can determine this:
1. Understand the total weight capacity: The shipping container has a weight capacity of 23,000 kilograms.
2. Account for already loaded weight: The container already has shipments weighing 3,800 kilograms.
3. Calculate remaining capacity: Subtract the weight of the other shipments from the total capacity to find out how much weight you can still add:
[tex]\[
\text{Remaining weight capacity} = 23,000 - 3,800 = 19,200 \text{ kilograms}
\][/tex]
4. Determine crate weight: Each crate weighs 110 kilograms.
5. Set up the inequality: To find the greatest number of crates [tex]\( c \)[/tex], you want the total weight of these crates plus the already loaded shipments to remain within the 23,000-kilogram limit:
[tex]\[
3,800 + 110c \leq 23,000
\][/tex]
6. Solve the inequality: Subtract 3,800 from 23,000 to find out how much weight can be dedicated to the crates:
[tex]\[
110c \leq 19,200
\][/tex]
Now, divide both sides by 110 to solve for [tex]\( c \)[/tex]:
[tex]\[
c \leq \frac{19,200}{110}
\][/tex]
Performing the division gives:
[tex]\[
c \leq 174.5454\ldots
\][/tex]
7. Determine the greatest whole number: Since [tex]\( c \)[/tex] must be a whole number, we need the largest integer value that satisfies the inequality:
[tex]\[
c \leq 174
\][/tex]
Therefore, the greatest number of 110-kilogram crates that can be loaded into the shipping container is 174. The correct inequality to express this situation is [tex]\( 23,000 \geq 3,800 + 110c \)[/tex].
