In gymnastics competition, an athlete's final score is calculated 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. What artistic score does the gymnast need to have a final score of at least 8.0?

The gymnast needs an artistic score of 9.2 to have a final score of at least 8

Step-by-step 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