To determine how many boxes are needed and how many popped kernels are in the last box, we'll first find out how many popped kernels are obtained from a pound of popcorn.
Given:
- There are 1450 kernels in a pound of unpopped popcorn.
- Each box holds 130 popped kernels.
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Calculate the total number of popped kernels: From the problem, we know that 1 pound of unpopped popcorn yields 1450 popped kernels when popped.
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Determine the number of full boxes (excluding the last box): We can divide the total number of popped kernels by the number of kernels each box can hold: \[ \text{Number of full boxes} = \left\lfloor \frac{1450}{130} \right\rfloor \] Performing the division: \[ \frac{1450}{130} \approx 11.1538 \] Taking the floor of this result, we find: \[ \left\lfloor 11.1538 \right\rfloor = 11 \] So, 11 full boxes can be filled.
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Calculate the number of kernels used in the full boxes: The total number of kernels in 11 boxes is: \[ 11 \times 130 = 1430 \]
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Calculate the number of popped kernels left for the last box: To find out how many kernels are left for the last box, subtract the number used for the full boxes from the total: \[ \text{Kernels left} = 1450 - 1430 = 20 \]
In conclusion:
- Number of boxes needed: 11 full boxes and 1 additional last box.
- Number of popped kernels in the last box: 20 kernels.
So, we have 12 boxes needed in total, with the last box containing 20 popped kernels.
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