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28 February, 09:07

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?

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  1. 28 February, 09:17
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    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
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