Chapter 1.5, Problem 22PPS

To determine

To find: the artistic score the gymnast does need to have a final score of at least 8.0.

Answer to Problem 22PPS

Artistic score that gymnast has to have is at least 9.2 to have final score greater or equal than 8.

Explanation of Solution

Given information:

An athlete’s final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score. All score are out of 10, and one gymnast has a 7.6 average technical score.

Calculation:

If average technical score is 75% of final score, and our gymnast had 7.6 on average technical score that means his score is

  $7.6\cdot \frac{75}{100}=5.7$

Now, when calculated that, can create inequality where will solve for what $x$ will gymnast have score greater or equal than 8.

  $\begin{array}{c}5.7+\frac{25}{100}x\ge 8.0\\ \frac{25}{100}x\ge 2.3\\ 25x\ge 100\cdot 2.3\\ x\ge 9.2\end{array}$

Artistic score that gymnast has to have is at least 9.2 to have final score greater or equal than 8.