Question

On the last 5 quizzes, Marco has earned a total of 21 out of 25 possible points. If he has a perfectscore on the next several quizzes, exactly how many points will he need to bring his average up to90%?(a) Write a rational equation to represent this situation.(b) Solve the equation, how many more points does Marco need to raise his percent to 90%?Show all work/steps

Answer 1

a.

We know that the average is given by the sum of the results divided by the total possible points, let x be the points of the last several quizzes since he already has 21 points its total points if he achieves a perfect score in the remaining quizzes is 21+x; the total would be 25+x and we want the average to be 90% then the equation we need is:

$\frac{x+21}{x+25}=0.9$

b.

Let's solve the equations:

$\begin{gathered} \frac{x+21}{x+25}=0.9 \\ x+21=0.9(x+25) \\ x+21=0.9x+22.5 \\ x-0.9x=22.5-21 \\ 0.1x=1.5 \\ x=\frac{1.5}{0.1} \\ x=15 \end{gathered}$

Therefore he needs 15 points to achieve 90%