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 1,450 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? a. 120 boxes with 20 popped kernels in the last box b. 11 boxes with 130 popped kernels in the last box c. 12 boxes with 20 popped kernels in the last box d. 11 boxes with 20 popped kernels in the last box
The Correct Answer and Explanation is:
To solve this problem, we start by understanding the relationship between the total number of unpopped kernels and how they fill the popcorn boxes once they are popped.
Step 1: Understand the given data
- 1 pound of unpopped popcorn contains 1,450 kernels.
- Each popcorn box holds 130 popped kernels.
- We’re asked to figure out:
- How many full boxes of popcorn can be filled?
- How many kernels are in the last (not completely filled) box?
Step 2: Divide to find number of full boxes
We divide the total number of popped kernels by the capacity of each box: 1450130=11 R 20\frac{1450}{130} = 11 \text{ R } 201301450=11 R 20
This means:
- We can fill 11 full boxes (each with 130 kernels).
- There are 20 popped kernels left over, which go into the last (incomplete) box.
Step 3: Answer the question
- Number of full boxes: 11
- Number of kernels in the last (not full) box: 20
Final Answer:
d. 11 boxes with 20 popped kernels in the last box
Explanation:
This problem involves division with a remainder to determine how a fixed quantity is distributed evenly into smaller units, with a final partial unit left over. We are given that one pound of unpopped popcorn contains 1,450 kernels. When these kernels are popped, they are placed into boxes, with each box capable of holding 130 popped kernels.
To determine how many boxes are needed, we divide the total number of kernels (1,450) by the capacity of each box (130). The division results in 11 complete groups (or full boxes) and a remainder of 20 kernels. This means that after filling 11 full boxes, 20 popped kernels are left. These do not fill another complete box, but they are still placed in an additional (partial) box.
Thus, in total, we need 12 boxes: 11 full boxes and 1 additional box containing only 20 popped kernels. This illustrates the concept of quotient and remainder in division. The quotient (11) represents how many full units we can make, and the remainder (20) represents what’s left over that doesn’t complete another full unit.
Among the multiple-choice options, only choice (d) correctly states that 11 boxes are fully filled and that the last box contains 20 popped kernels. All other choices either misstate the number of boxes or the number of kernels in the last box. Therefore, the correct answer is:
d. 11 boxes with 20 popped kernels in the last box.
