Answer:
The gymnast needs an artistic score of 9.2 to have a final score of at least 8
Explanation:
* Lets explain how to solve the problem
- In gymnastics competition the athlete’s final score is calculated
by taking 75% of the average technical score and adding 25%
of the artistic score
∴ The final score = 75% of average technical score + 25% of artistic
score
- All scores are out of 10
- One gymnast has a 7.6 average technical score
∴ The average technical score = 7.6
- The gymnast need to have a final score of at least 8.0
∴ The final score is 8.0
∵ The final score = 75% of average technical score + 25% of artistic
score
∵ The average technical score = 7.6
∵ The final score is 8.0
- Substitute these values in the equation above
∴ 8 = 75% (7.6) + 25% of artistic score
∴ 8 = 75/100 (7.6) + 25/100 of artistic score
∴ 8 = 0.75(7.6) + 0.25 of artistic score
∴ 8 = 5.7 + 0.25 of artistic score
- Subtract both sides by 5.7
∴ 2.3 = 0.25 of artistic score
- Divide the both sides by 0.25
∴ The artistic score = 9.2
* The gymnast needs an artistic score of 9.2 to have a final score of
at least 8