Question

a student has an average of 76 on the first 5 quizzes, what average is needed on the next 5 quizzes to pull his quiz average up to an 80?

Answer 1

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.

`(x+x+x+x+x)/(5)=76`

You can find the dividend by cross multiplying.

`(x+x+x+x+x)/(5)=76 \rightarrow x+x+x+x+x=76 *5 \rightarrow 380`

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).

`80 * 10=800`

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:

`800-380=420`

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:

`420 / 5=84`

Your answer is 84(84%).