Final answer:
Selena's reasoning is incorrect because to determine how much each person gets, the ratios must be simplified to find the per-person share. After simplifying, it's clear that a person at the small table (8:3 ratio) gets slightly more pizza than a person at the large table (10:4 ratio).
Step-by-step explanation:
Selena is trying to determine whether a person at a small table or large table gets more based on the ratios 8:3 and 10:4. We can assess this by simplifying the ratios to understand the amount each person gets.
For the small table, the ratio of 8:3 means that for every 8 units of pizza available, 3 people will share them. Thus, each person at the small table gets ⅓ (8 divided by 3) units of pizza.
For the large table, the ratio of 10:4 suggests that for every 10 units of pizza, 4 people will share them, so each person at the large table gets ⅔ (10 divided by 4) units of pizza.
Upon converting these to decimals, ⅓ is approximately 2.67, and ⅔ is 2.5.
Therefore, a person at the small table gets slightly more pizza than a person at the large table.
However, Selena's reasoning based on the difference between the numbers in the ratios is not correct.
When analyzing ratios, we are interested in the proportional relationship between the numbers, not just the raw difference. In fact, when she states that 'The large table has more people so the people at the small table will get more pizza,' she's making an assumption that doesn't align with how ratios work.
The correct approach is to compare the per-person share at each table by simplifying the ratios, as we did above.