Question

A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 130
popped kernels. There are 1450
kernels in a pound of unpopped popcorn. If all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last box?

Answer 1

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.

1. **Calculate the total number of popped kernels:**
From the problem, we know that 1 pound of unpopped popcorn yields 1450 popped kernels when popped.

2. **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.

3. **Calculate the number of kernels used in the full boxes:**
The total number of kernels in 11 boxes is:
\[
11 \times 130 = 1430
\]

4. **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**.