A 10-yr-old competes in gymnastics. For several competitions she received the following "All-Around" scores: 36.3, 37.9, 37.1, and 36.1. Her coach recommends that gymnasts whose "All-Around" scores average at least 35.2 move up to next level. What "All-Around" scores in the next competition would result in the child being eligible to move up?
To find the average of the scores, we need to add them up and divide by the number of scores.
Average score = (36.3 + 37.9 + 37.1 + 36.1) / 4 = 147.4 / 4 = 36.85
To be eligible to move up to the next level, the average score needs to be at least 35.2.
To find the score needed in the next competition, we can set up the following equation:
(36.3 + 37.9 + 37.1 + 36.1 + x) / 5 = 35.2
Multiplying both sides of the equation by 5, we get:
36.3 + 37.9 + 37.1 + 36.1 + x = 176
Simplifying the equation, we get:
147.4 + x = 176
Subtracting 147.4 from both sides, we get:
x = 176 - 147.4
x = 28.6
Therefore, to be eligible to move up to the next level, the gymnast would need an "All-Around" score of at least 28.6 in the next competition.