Answer:
The total number of boys is 12 and total number of girls is 27 at the birthday party.
Step-by-step explanation:
Let x be the total number of boys and y be the total number of girls.
ATP,
Boys/Girls = 4/9
=> x/y = 4/9 ...(Cross multiply)
=> 9x = 4y ...(1)
Now when 17 girls left,
(x)/(y-17) = 6/5
5x = 6y-102 ...(2)
From (1) we have x = 4y/9(Divide both sides by 9)
Substitute the value of x in eqn (2):
=> 5*4y/9 = 6y-102
=> 20y/9 = 6y -102
Rearrange terms:
=> 6y-20y/9 = 102
Take LCM:
=> (54y-20y)/9 = 102
=> 34y = 102*9 (Multiply both sides by 9)
=> y = 102*9/34 (Divide both sides by 34)
=> y = 3*9 = 27
From (1) ,
x = 4*27/9 = 4*3 = 12
So the total number of boys is 12 and total number of girls is 27 at the birthday party.
