# math

4/9of a group of students are girls .if there are 17more boys than girls ,how many students are there altogether

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1. S = number of students

g = number of girls

b = number of boys

b = g + 17

S = g + b

S = g + g + 17

S = 2 g + 17

g = 4 / 9 S so :

S = 2 * ( 4 / 9 ) S + 17

S = ( 8 / 9 ) S + 17 Subtract ( 8 / 9 ) S to both sides

S - ( 8 / 9 ) S = ( 8 / 9 ) S + 17 - ( 8 / 9 ) S

( 9 / 9 ) S - ( 8 / 9 ) S = 17

( 1 / 9 ) S = 17 Multiply both sides by 9

S = 153

Proof :

g = ( 4 / 9 ) * 153 = 4 * 153 / 9 = 612 / 9 = 68

b = S - g = 153 - 68 = 85

b - g = 85 - 68 = 17

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