Using averges to find the total

• May 17th 2007, 11:34 AM
Using averges to find the total
Jane and Mitzi have both done the same number of practice papers for their mathematics examination.
They both have the same total mark, T.
They do one more practice paper.
Jane scores 89 and her average score increses to 68.
Mitzi scores 57 and her average score decreases to 64.

Find the final number of practice papers taken by each student.

-How would I work this one out, thanks.
• May 17th 2007, 11:42 AM
CaptainBlack
Quote:

Jane and Mitzi have both done the same number of practice papers for their mathematics examination.
They both have the same total mark, T.
They do one more practice paper.
Jane scores 89 and her average score increses to 68.
Mitzi scores 57 and her average score decreases to 64.

Find the final number of practice papers taken by each student.

-How would I work this one out, thanks.

Let the number of papers be N.

After the extra paper we have for Jane:

68 = (T + 89)/(N+1)

and for Mitzi:

64 = (T+ 57)/(N+1)

or rearranging:

68N - T = 21
64N - T = -7

which you may solve to find that N = 7.

RonL
• May 17th 2007, 12:03 PM
Jane
68N + 68 = T + 89

68N + 68 - 89 = T

68N - 21 = T

Substituted this into second equation:

64N + 64 = T + 57

64N + 64 = 68N - 21 + 57

64N - 68N = -21 + 57 - 64

-4N = -28

N = -28/4

N = -7

Wrong? Also, the answer in the practice paper is 8.
• May 17th 2007, 12:09 PM
CaptainBlack
Quote:

Jane
68N + 68 = T + 89

68N + 68 - 89 = T

68N - 21 = T

Substituted this into second equation:

64N + 64 = T + 57

64N + 64 = 68N - 21 + 57

64N - 68N = -21 + 57 - 64

-4N = -28

N = -28/4

N = -7

Wrong? Also, the answer in the practice paper is 8.

I solved for N, which is the number of papers before the extra one.
I should have made that clearer.

RonL
• May 17th 2007, 12:11 PM
CaptainBlack
Quote:

Jane
68N + 68 = T + 89

68N + 68 - 89 = T

68N - 21 = T

Substituted this into second equation:

64N + 64 = T + 57

64N + 64 = 68N - 21 + 57

64N - 68N = -21 + 57 - 64

-4N = -28

N = -28/4

No, -4N = -28, so 4N = 28, or N=7.

Quote:

N = -7

Wrong? Also, the answer in the practice paper is 8.
• May 17th 2007, 01:55 PM
Soroban

Let's start this again . . .

Quote:

Jane and Mitzi have both done the same number of practice papers.
They both have the same total mark, T.
They do one more practice paper.
Jane scores 89 and her average score increases to 68.
Mitzi scores 57 and her average score decreases to 64.

Find the final number of practice papers taken by each student.

Let N = final number of practice papers.

Jane has a total of T points and scores 89 more.
Her average is 68: .(T + 89)/N .= .68 . . . . 68N - T .= .89 .[1]

Mitzi has a total of T points and scores 57 more.
Her average is 57: .(T + 57)/N .= .64 . . . . 64N - T .= .57 .[2]

Subtract [2] from [1]: . 4N = 32 . . . . N = 8

Therefore, they each took 8 practice papers.