The school nutritionist is ordering apples for school lunches. The price for six crates of apples delivered to the school is $82. The price for 11 crates is $137. By how much does the cost increase for each additional crate of apples purchased?

Question

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$5
$11
$27
$55

Answer 1

To find the cost increase for each additional crate of apples purchased, we first need to determine the cost per crate based on the given information.

1. Calculate the cost per crate for 6 crates: \[ \text{Cost for 6 crates} = 82 \] \[ \text{Cost per crate} = \frac{82}{6} \approx 13.67 \]

2. Calculate the cost per crate for 11 crates: \[ \text{Cost for 11 crates} = 137 \] \[ \text{Cost per crate} = \frac{137}{11} \approx 12.45 \]

3. Calculate the difference in cost per crate between 11 crates and 6 crates:

   • From earlier calculations:
     • Cost per crate for 6 crates is approximately $13.67
     • Cost per crate for 11 crates is approximately $12.45

4. Find the average cost increase per crate: \[ \text{Cost for 6 crates} = 82 \] \[ \text{Cost for 11 crates} = 137 \]

   \[ \text{Difference in total cost} = 137 - 82 = 55 \] \[ \text{Difference in number of crates} = 11 - 6 = 5 \]

   Thus, the average cost increase per additional crate is: \[ \text{Cost increase per crate} = \frac{55}{5} = 11 \]

The cost increases by $11 for each additional crate of apples purchased.

Final Answer: $11