SOLUTION: There are 170 people in the hall. 3/5 of the males were boys and 4/9 of the females were girls. There were a total of 82 adults. a) Find the number of girls. b) Find the number

Algebra ->  Probability-and-statistics -> SOLUTION: There are 170 people in the hall. 3/5 of the males were boys and 4/9 of the females were girls. There were a total of 82 adults. a) Find the number of girls. b) Find the number      Log On


   

Question 838959: There are 170 people in the hall. 3/5 of the males were boys and 4/9 of the females were girls. There were a total of 82 adults.
a) Find the number of girls.
b) Find the number of men.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

There are 170 people in the hall. f + m = 170  0r+m+=+%28170-f%29

    3/5 of the males were boys (%282%2F5%29 of the males were men)

and 4/9 of the females were girls (%285%2F9%29 of the females were women)

Question states*** There were a total of 82 adults. 

  women    +     men = 82

 %285%2F9%29f+%2B+%282%2F5%29m+=+82   |Substituting for m

 %285%2F9%29f+%2B+%282%2F5%29%28170-f%29+=+82   ||Multiplying thru by 45 so as all denominators = 1

   25f + 18(170-f) = 82*45

        7f = 82*45 - 18*170

        f = 90, number of females, 80 the number of males  (170-90)

a) Find the number of girls %284%2F9%2990+=+highlight%2840%29

b) Find the number of men  %282%2F5%2980+=+highlight%2832%29

CHECKING our answer***Note: 50 women and 48 boys

40 + 50  +  32 + 48 = 170

Wish You the Best in your Studies.