SOLUTION: if a ratio of buses to trucks is 5:3, and then k buses arrive to make the ratio 9:5, find in terms of k, the total number of trucks and buses present

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: if a ratio of buses to trucks is 5:3, and then k buses arrive to make the ratio 9:5, find in terms of k, the total number of trucks and buses present       Log On


   

Question 1146633: if a ratio of buses to trucks is 5:3, and then k buses arrive to make the ratio 9:5, find in terms of k, the total number of trucks and buses present
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
system%28b%2Ft=5%2F3%2C%28b%2Bk%29%2Ft=9%2F5%29

system%28b=5t%2F3%2C9t=5b%2B5k%29

9t-5b=5k
9t-5t%2F3=5k
t%289-5%2F3%29=5k

t%2827%2F3-5%2F3%29=5k

t%2822%2F3%29=5k
highlight%28t=15k%2F22%29
--
b=5t%2F3=%285%2F3%29%2815k%2F22%29
highlight%28b=25k%2F22%29

Those are the original quantities, before the k buses arrived.


--

If you want to answer question:
find in terms of k, the total number of trucks and buses present?

This will include the k vehicles which arrived.
b%2Bt%2Bk
%2815%2F22%29k%2B%2825%2F22%29k%2Bk-------and you can simplify this.