Question

A math contest question says: "Unfortunately, you missed the last math test in your class because you were ill. Your score of a 96 raised the class average from 71 to 72. How many students including yourself are in your class?"
First of all, It says you missed the test while still saying afterwards that you got a score of 96.
And second, how should I find the answer when having such limited information (I don't want the answer I only need help)

Answer 1

i think it means that you missed the test, the average was 71, then you took it late, scored 96 and raised the average to 72
as for solving, you want the number of people in the class so start by introducing a variable, say \(n\) is the number of people in the class and write two expressions for \(n\) using the two averages

Answer 2

if you want a further hint let me know

Answer 3

Hmm, there are [Math Processing Error] in your reply...

Answer 4

refresh your browser

Answer 5

i wrote "n" as the number of students in the class

Answer 6

Ok, I'll try to get the answer, If I can't, I'm going to ask for further help. Thanks.

Answer 7

ok

Answer 8

To find the average, it is: 1/3(score1 + score2 + score3), so how do I reverse this operation to find the number of students?

Answer 9

ok lets try this. call the class total before you took the exam \(X\) and of course the total after the exam is \(X+96\)

Answer 10

Define these two variables.
S = sum of scores before your test
n = number of students besides you
Think about writing two equations. Each one represents the mean before and after you took it, remembereing that
mean = total sum / total number

Answer 11

Those two equations shouldn't be too hard for you to write. Once you write them, it's a simple matter to solve for n.

Answer 12

then the average before you took the exam is \[\frac{X}{n-1}\] and the average after you took the exam is \[\frac{X+96}{n}\] and you know what both of these numbers are, 71 and 72 respectively so set
\[\frac{X}{n-1}=71\] and
\[\frac{X+96}{n}=72\] ad solve for \(n\)

Answer 13

oh, what smoothmath said!

Answer 14

btw this kind of question comes up repeatedly on exams for education majors

Answer 15

So it's 24 students not including you because: 24 * 71 = 1704, and that plus 96 = 1800, now 1800 / 25 = 72

Answer 16

is that right?

Answer 17

if you checked the answer and it works, it has to be right

Answer 18

How did you get from
X+96 over n = 71 to 1704/71= 24? i think I'm missing a big step and i can't seem to get any answer through x over n-1 = 71 and x+96 over n=72.