The student has an average of 76 on his first 5 quizzes. Remember that average is also known as mean. Mean is calculated by adding the values in a data set and dividing it by the amount of numbers you added.
In this case,the mean is 76. That means five numbers were added and divided by 5 and the quotient was 76.
[tex]\frac{x+x+x+x+x}{5}=76[/tex]
You can find the dividend by cross multiplying.
[tex]\frac{x+x+x+x+x}{5}=76 \rightarrow x+x+x+x+x=76 \times5 \rightarrow 380[/tex]
The total points he got on his first 5 quizzes was 380.
If he wants to boost his average grade up to an 8 after taking another 5 quizzes, you need to multiply his average goal by the amount of quizzes, which is 10(5+5=10).
[tex]80 \times 10=800[/tex]
His total points after taking all his quizzes(that is, if he reached his goal) should be 800. Because he already took 5 quizzes and got a total score of 380, you're going to subtract 380 from 800 and divide it by the remaining quizzes left, which is 5.
First subtract 380 from 800:
[tex]800-380=420[/tex]
That means his next 5 quizzes need to sum up to a total of 420 points. Since you're trying to find the average of his next 5 quizzes in order to average up to an 80, you need to divide 420 by 5(number of remaining quizzes).
Divide:
[tex]420 \div 5=84[/tex]
Your answer is 84(84%).
