Respuesta :
From the statement, we know that in the last 5 quizzes, Marco has earned 21 out of 25 possible points. If each quiz gives Marco the same possible points, each quiz can give Marco s = 5 possible points. We can write the following formula for the average:
[tex]A=\frac{S_1+S_2+\ldots+S_N}{s\cdot N}\cdot100[/tex]Where:
• S_1, S_2, ... are the scores that Marco obtains in each quiz,
,• N is the total number of quizzes played by Marco,
,• s = 5 is the max possible points that Marco can win in each quiz,
,• the 100 is a factor to convert the average to %.
Now, we know that Marco obtained:
[tex]S_1+S_2+S_3+S_4+S_5=21[/tex]points in the 5 first quizzes.
If Marco has a perfect score on the next several quizzes, he will get:
[tex]S_i=5,i\ge6.[/tex]We must find how many points he will need to get an average A = 90.
We replace the data that we know in the formula above:
[tex]\begin{gathered} \frac{(S_1+S_2+S_3+S_4+S_5)+(S_6+\cdots_{}+S_N)}{s\cdot N}\cdot100=90, \\ \frac{21+5\cdot(N-5)}{5\cdot N}\cdot100=90. \end{gathered}[/tex]We solve the last equation for N:
[tex]\begin{gathered} \frac{21+5N-25}{5N}\cdot100=90, \\ \frac{5N-4}{5N}=0.9, \\ 5N-4=0.9\cdot5N, \\ 5N-4=4.5N, \\ 0.5N=4, \\ N=\frac{4}{0.5}=8. \end{gathered}[/tex]So Marco needs to play 48 games. The total points that he needs to play are:
[tex]P=21+5(N-5)=21+5(8-5)=21+5\cdot3=36[/tex]Answer: Marco will need to have 36 points in total in 8 quizzes to reach an average of 90%. He has played 5 quizzes and obtained 21 out of 25 possible points. So he will need to play 3 additional games with a perfect score of 5, getting 15 points to reach the average of 90%.
