Algebra 2 Question

Question

A group of students take a test and the average score is 66. One more student takes the test and receives a score of 82 increasing the average score of the group to 68. How many students were in the initial group?

Answer 1

For the intial group with x students, the avg. was 66, so their total score must have been 66x since

avg = total/x.

For the larger group, there are now x +1 students with an avg, of 68,so their test score total was 68(x + 1)

We know that the added student had an 82, so the difference in total test scores must be 82.

Therefore 82 = 68(x + 1) - 66x

82 = 68x + 68 - 66x → 82 - 68 = 2x → 14 = 2x x = 7

Check: 66(7) = 462

68(8) = 544

82

Answer 2

Ok so we know that the initial group has an average score of 66. So we can set the sum to be m and the number of students to be n. So we know that m/n=66.

Now we know that another student took the test and got an 82 and increased the score from 66 to 68. So we then have this equation for the updated group:

(m+82)/(n+1)=68

So then we can set m=66n for our first equation and our second equation to be m+82=68(n+1)

Now we have a system of equations:

m=66n

m+82=68n+68

Next step:

m=66n

m=68n-14

So now we can set 66n=68n-14, which also gets us -2n=-14

We divide both sides by -2 and find that n=7.

So then we can plug everything in now.

m/7=66 -> 462=m for the initial group.

Then m+82/(7+1)=68

(462+82)/8= 544/8= 68

Bam! There you go!