need help with ratios and rates

Question

Of people attending the concert there were 3 adults for every 8 teenagers and 1 senior citizen for every 4 teenagers. In all, 572 people attended the concert. How many people in each age category attended the concert?

Answer 1

Let A represent Adults

     T teenagers and S seniors

3A=8T

1S=4T, therefore 2S=8T (8/4=2)

 

2S=3A=8T

 

2+3+8=13 

 

572/13=44 times

 

teenagers=8*44=352

adults        3*44=132

seniors       2*44=88

 

 

 

Answer 2

3 adults for every 8 teenagers

1 senior citizen for every 4 teenagers, which means 2 senior citizens for every 8 teenagers

the ratio of adults to teenagers to senior citizens is 3 to 8 to 2

3+8+2=13

572/13=44

44*3=132 adults

44*8=352 teenagers

44*2=88 senior citizens