Question

In a gymnastics competition, an athlete's final score is found by taking 75% of the average technical score and adding 25% of the artistic score. All scores are out of 10, and one gymnast has a 7.6 average technical score. Write an inequality that you would use to determine the artistic score, x, that the gymnast needs to earn in order to have a final score of at least 8.0. Do not solve this inequality.

Answer 1

5.7 + 2.5/10x ≥ 8

where x is the artistic score

Explanation:

if the technical score is 7.6/10 = 76% of 75% = 0.57 out of 10.

there are still 2.5 more points that can be obtained, so the gymnast needs 8 - 5.7 = 2.3 out of 2.5 possible points

the inequality would be:

5.7 + 2.5/10x ≥ 8

where x is the artistic score

2.5/10x ≥ 8 - 5.7

2.5/10x ≥ 2.3

x ≥ (2.3 x 10) / 2.5

x ≥ 9.2