Question

In another contest Trey got a prize point for every 3 tickets he sold. Trey sold 271 tickets as got the sam numbers of prize points as Kim

90. Explain why this is true bye showing your work.

Answer 1

Trey and Kim both received the same number of prize points because Trey sold 271 tickets, and for every 3 tickets sold, he earned one prize point. Therefore, 271 ÷ 3 = 90, which is the number of prize points Trey received, matching Kim's total.

Step-by-step explanation:

Trey's prize points are determined by the number of tickets he sold, with one point awarded for every three tickets. To find the total number of prize points Trey earned, we divide the total number of tickets sold (271) by the ratio of tickets to points (3).

The calculation is as follows:

`\[ (271)/(3) = 90. \]`

This means Trey earned 90 prize points. Now, the crucial point is that Kim also received the same number of prize points. This indicates that the relationship between the number of tickets sold and prize points earned is consistent for both Trey and Kim. The fact that Trey sold 271 tickets aligns with him receiving 90 prize points, making it evident that Kim must have sold a similar number of tickets to achieve the same number of prize points.

In summary, the reasoning lies in the consistent conversion rate of tickets to prize points, where every 3 tickets yield 1 point. Trey's 271 tickets correspond to 90 prize points, leading to the conclusion that Kim sold a matching number of tickets to obtain the same number of prize points, resulting in the equality between their respective totals.