Question

If joseph gets 71 on his next test his average will be 83. If he gets 99, his average will be 87. How mamy tests has joseph taken?

Answer 1

Answer:

Joseph has taken 7 test

Step-by-step explanation:

Formula used:

$Average=\frac{sum\:of\:observations}{number\:of\:observations}$

Let $\Sigma{x}$ be the sum of the marks of joseph in previous tests.

Let n be the number of tests he has taken

case(i): If he gets 71 in the next test

$Average=\frac{sum\:of\:his\:marks}{n}$

$\implies\:83=\frac{\Sigma{x}+71}{n}$

$\implies\:\Sigma{x}+71=83n$............(1)

case(i): If he gets 99 in the next test

$Average=\frac{sum\:of\:his\:marks}{n}$

$\implies\:87=\frac{\Sigma{x}+99}{n}$

$\implies\:\Sigma{x}+99=87n$............(2)

(2)-(1)

$\implies\:(\Sigma{x}+99)-(\Sigma{x}+71)=87n-83n$

$\implies\:\Sigma{x}+99-\Sigma{x}-71=4n$

$\implies\:28=4n$

$\implies\:n=\frac{28}{4}$

$\implies\:n=7$

Answer 2

Answer:

Joseph has already taken 6 Tests

Step-by-step explanation:

If joseph gets 71 on his next test his average will be 83. If he gets 99, his average will be 87. How mamy tests has joseph taken?

Let say Joseph has taken n Tests & Marks obtained in n Test = M

If joseph gets 71 on his next test his marks would be M + 71

number of tests = n + 1

Average = Total Marks/ numbers of Tests

=>  83 = (M + 71)/(n + 1)

=> 83n + 83 = M + 71

=> 83n + 12 = M

If joseph gets 99 on his next test his marks would be M + 99

=>  87 = (M + 99)/(n + 1)

=> 87n + 87 = M + 99

=> 87n - 12 = M

Comparing Both

83n + 12 = 87n - 12

=> 4n = 24

=> n = 6

Joseph has already taken 6 Tests

Next test would be 7th Test