Final Answer:
Elizabeth can arrange her 35 toy cars on the top and bottom shelves of her bookcase in three ways: she can put 10 cars on the top shelf and 25 on the bottom, or distribute them evenly with 17 cars on each shelf, or opt for a combination such as 15 on the top shelf and 20 on the bottom.
Step-by-step explanation:
When deciding how to distribute the 35 toy cars on the top and bottom shelves, Elizabeth has several options. One approach is to have a larger portion on one shelf and a smaller portion on the other. For instance, putting 10 cars on the top shelf and 25 on the bottom gives a total of 35 cars. Alternatively, she can choose to distribute them more evenly, such as having 17 cars on each shelf. The sum of 17 and 17 is 34, so she would need to adjust slightly by placing one additional car on either the top or bottom shelf.
Additionally, Elizabeth could opt for a combination approach, like placing 15 cars on the top shelf and 20 on the bottom, providing flexibility in organizing her toy cars. These arrangements highlight the concept of partitioning a given quantity into two sets, and the multiple possibilities emphasize the flexibility in making choices based on personal preferences or the design of the bookcase.
Understanding these options allows Elizabeth to showcase her toy cars in a visually appealing and organized manner while utilizing the available shelf space effectively. The exercise provides a practical application of basic arithmetic and problem-solving skills in real-life scenarios, fostering a foundational understanding of mathematical concepts.