WHAT PERCENTAGE PASSED???
 
 
 Mr. Nazelli gave an examination in which the average mark of those passing is 65, while the average mark of those failing is 35. If the average mark of all participants is 53, what percentage of the participants passed?

Passing Average ( x ) = 65 marks

Failing Average ( y )=35 marks

Pass + Fail Average = 53 marks

Question How many pass ( % )

65 * x = 65x

35 * y = 35y

(65x + 35y) / x + y = 53

65x + 35y = 53x + 53y

65x + 35y - 53x - 53y =0

12x - 18y =0

12x = 18y

x= 18y / 12 ------ ( 1 )

sub

[ 65( 18y / 12 ) + 35y ] / [ ( 18y / 12 ) + y ] = 53

[ ( 1170y / 12 ) + 35y ] / [ ( 18y / 12] + y ] = 53

[ 1170 y + 420y ] / [ 18y + 12y ] = 636 { 52 * 12 }

1590y / 30y = 636

53y = 636

y= 12 sub into 1

x= 18 { 216 / 12 }

x + y = 30

Answer: ( 18 / 30 ) * 100 = 60 %