SOLUTION: I'm having trouble with this problem 30% of the seventh-graders and 40% of the eighth-graders went to the school dance. At the dance, the ratio of seventh to eighth graders was

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: I'm having trouble with this problem 30% of the seventh-graders and 40% of the eighth-graders went to the school dance. At the dance, the ratio of seventh to eighth graders was       Log On


   

Question 1099986: I'm having trouble with this problem
30% of the seventh-graders and 40% of the eighth-graders went to the school dance. At the dance, the ratio of seventh to eighth graders was 21:32. What is the ratio of seventh to eighth graders that did not go to the dance?
Thank you.
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let s = the number of the school seventh-graders and 
    e = the number of the school eight-graders.


We are given 


%280.3%2As%29%2F%280.4%2Ae%29 = 21%2F32,   or, equivalently,

%283%2As%29%2F%284%2Ae%29 = 21%2F32,

which implies 

s%2Fe = %2821%2A4%29%2F%2832%2A3%29 = 7%2F8.



The problem asks about  %28s-0.3%2As%29%2F%28e-0.4%2Ae%29.   This ratio is 


%28s-0.3%2As%29%2F%28e-0.4%2Ae%29 = %28s%2A%281-0.3%29%29%2F%28e%2A%281-0.4%29%29 = %280.7%2As%29%2F%280.6%2Ae%29 = %280.7%2F0.6%29%2A%28s%2Fe%29 = %280.7%2F0.6%29%2A%287%2F8%29 = 4.9%2F4.8 = 49%2F48.



Answer.  The ratio under the question is  49%2F48.