Question

You were sick and take a test a day late. Your 95 raised the class average from 69 to 70. How many students, including you, took the test?

Answer 1

Answer:

• 26

Explanation:

The average is the mean. It is calculated adding all the values and dividing the sum by the number of values (data):

For the students who took the test the day before you, you can write:

$mean_1=\sum scores/n$

Where n is the number of students who took the test first.

Thus, when the average was 69 the equation is:

$69=\sum scores/n$

When you take the test, the n + 1, the new average is 70, and the sum of the scores raised in 95 points:

$mean_2=(\sum scores + 95)/(n+1)\\ \\ 70=(\sum scores+95)/(n+1)$

Now you have a system of two equation and two unknowns, so you can solve it.

Clear the sum of the scores from the first equation:

$69=\sum scores/n=>\sum scores=69n$

Subsitute in the second equation:

$70=(69n+95)/(n+1)$

Solve for n:

$70(n+1)=69n+95\\ \\ 70n+70=69n+95\\ \\ 70n-69n=95-70\\ \\ n=25$

Thus, when you include your self the number of students who took the test was 25 + 1 = 26.