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?
? 11 ?boxes, 10 ?of them filled and 20 ?popped kernels in the last box
11 ?boxes
120 ?boxes with 20 ?popped kernels in the last partially filled box
12 ?boxes, eleven of them filled and 20 ?popped kernels in the last box
The correct answer and explanation is:
To solve the problem, we first need to understand the relationship between unpopped kernels, popped kernels, and the number of boxes.
Step 1: Converting unpopped kernels to popped kernels
The question tells us that 1 pound of unpopped popcorn has 1,450 kernels. When these kernels are popped, they expand. Typically, 1 unpopped kernel will yield approximately 3 popped kernels. Therefore, the total number of popped kernels in 1 pound of unpopped popcorn can be calculated as follows: Total popped kernels=1450×3=4350 popped kernels\text{Total popped kernels} = 1450 \times 3 = 4350 \text{ popped kernels}
Step 2: Determining how many boxes are needed
Each popcorn box holds 130 popped kernels. To find how many boxes are needed to hold all 4,350 popped kernels, we divide the total number of popped kernels by the number of popped kernels each box can hold: Number of boxes=4350130=33.46\text{Number of boxes} = \frac{4350}{130} = 33.46
Since we can’t have a fraction of a box, we round up to the nearest whole number, which gives us 34 boxes in total.
Step 3: Determining how many filled boxes and partially filled box
Out of these 34 boxes, we know that 33 will be fully filled with 130 popped kernels each. To determine how many popped kernels are in the last box, we calculate the remaining popped kernels: Remaining popped kernels=4350−(33×130)=4350−4290=60 popped kernels\text{Remaining popped kernels} = 4350 – (33 \times 130) = 4350 – 4290 = 60 \text{ popped kernels}
So, the last box will have 60 popped kernels.
Final Answer:
- The total number of boxes needed is 34.
- 33 boxes will be filled with 130 popped kernels each.
- The last (34th) box will contain 60 popped kernels.
Thus, the correct answer is:
34 boxes in total, with 33 filled and 60 popped kernels in the last box.