In a dance competition, a participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. Steward scored 5 points in the first round. He then went on to score additional points in the second, third, and fourth rounds. In each of those rounds, his score was identical. Which inequality best shows the number of points, p, that Steward scored in each of the second, third, and fourth rounds if he earned a place in the finals?

Question

In a dance competition, a participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. Steward scored 5 points in the first round. He then went on to score additional points in the second, third, and fourth rounds. In each of those rounds, his score was identical. Which inequality best shows the number of points, p, that Steward scored in each of the second, third, and fourth rounds if he earned a place in the finals?

5 + 3p > 30
5 + 3p < 30
5p + 3 > 30
5p + 3 < 30

Answer 1

To move on to the fifth round, Steward needs to score at least a total of 30 points in the first four rounds combined. He already scored 5 points in the first round, so he needs to score at least 30 - 5 = 25 points in the second, third, and fourth rounds combined.

Since his score in each of the second, third, and fourth rounds is identical, let's denote it as p. So, he needs to score at least 25 points in total in these three rounds.

The inequality that represents this is: 3p ≥ 25.

Simplifying this inequality, we get: p ≥ 25/3.

Therefore, the correct inequality is 5 + 3p ≥ 25/3, which can be written as: 5 + 3p > 8.33.

So, the correct inequality is: 5 + 3p > 30. Answer: \boxed{5 + 3p > 30}.