Fruit juice boxes are packed into a larger box so that it can be transported to shops without damage.

| Dimensions of 1 juice box | Dimensions of 1 Large box |
| :------------------------- | :----------------------- |
| Length = 4.5 cm | Length = 50 cm |
| Width = 3.5 cm | Width = 30 cm |
| Height = 6 cm | Height = 35 cm |

The juice boxes can be packed into the larger boxes in two ways:

In option 1, the length of the juice box is packed into the length of the larger box. In option 2, the width of the juice box is packed into the length of the larger box.

3.1 Determine how many juice boxes can fit into the larger box for option 1.

3.2 Determine how many juice boxes can fit into the larger box for option 2.

Calculate the number of juice boxes that fit along the length, width, and height for Option 1: ⌊ 4.5 50 ​ ⌋ = 11 , ⌊ 3.5 30 ​ ⌋ = 8 , ⌊ 6 35 ​ ⌋ = 5 .
Determine the total number of juice boxes for Option 1: 11 × 8 × 5 = 440 .
Calculate the number of juice boxes that fit along the length, width, and height for Option 2: ⌊ 3.5 50 ​ ⌋ = 14 , ⌊ 4.5 30 ​ ⌋ = 6 , ⌊ 6 35 ​ ⌋ = 5 .
Determine the total number of juice boxes for Option 2: 14 × 6 × 5 = 420 . 440 , 420 ​

Explanation

Problem Analysis We are given the dimensions of a juice box and a larger box. The goal is to determine how many juice boxes can fit into the larger box in two different packing options. In option 1, the length of the juice box (4.5 cm) aligns with the length of the larger box (50 cm). In option 2, the width of the juice box (3.5 cm) aligns with the length of the larger box (50 cm).

Option 1: Packing Strategy For option 1, we need to calculate how many juice boxes fit along the length, width, and height of the larger box. We do this by dividing the dimensions of the larger box by the corresponding dimensions of the juice box and taking the integer part (floor) of the result.

Option 1: Calculations Number of juice boxes along the length: ⌊ 4.5 50 ​ ⌋ = ⌊ 11.11 ⌋ = 11 Number of juice boxes along the width: ⌊ 3.5 30 ​ ⌋ = ⌊ 8.57 ⌋ = 8 Number of juice boxes along the height: ⌊ 6 35 ​ ⌋ = ⌊ 5.83 ⌋ = 5

Option 1: Total Count Total number of juice boxes for option 1: 11 × 8 × 5 = 440

Option 2: Packing Strategy For option 2, we again calculate how many juice boxes fit along the length, width, and height of the larger box. This time, the width of the juice box is aligned with the length of the larger box.

Option 2: Calculations Number of juice boxes along the length: ⌊ 3.5 50 ​ ⌋ = ⌊ 14.29 ⌋ = 14 Number of juice boxes along the width: ⌊ 4.5 30 ​ ⌋ = ⌊ 6.67 ⌋ = 6 Number of juice boxes along the height: ⌊ 6 35 ​ ⌋ = ⌊ 5.83 ⌋ = 5

Option 2: Total Count Total number of juice boxes for option 2: 14 × 6 × 5 = 420

Final Answer Therefore, for option 1, 440 juice boxes can fit into the larger box, and for option 2, 420 juice boxes can fit into the larger box.


Examples
When planning shipments of goods, understanding how many items can fit into a container is crucial for optimizing transportation costs. For example, a logistics company needs to transport juice boxes to various stores. By calculating the most efficient way to pack the juice boxes into larger containers, the company can minimize the number of containers used, thereby reducing shipping expenses and environmental impact. This problem demonstrates how to maximize space utilization in real-world scenarios.

Answered by GinnyAnswer | 2025-07-08

A total of 440 juice boxes can fit into the larger box using option 1 (juice box length aligned with box length), and 420 juice boxes can fit using option 2 (juice box width aligned with box length).
;

Answered by Anonymous | 2025-07-27