SOLUTION: The quantities S and T are positive and are related by the equation S=k/T, where k is a constant. If the value of S increases by 50 percent, then the value of T decreases by what p

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The quantities S and T are positive and are related by the equation S=k/T, where k is a constant. If the value of S increases by 50 percent, then the value of T decreases by what p      Log On


   

Question 510688: The quantities S and T are positive and are related by the equation S=k/T, where k is a constant. If the value of S increases by 50 percent, then the value of T decreases by what percent?
I figured 50% but the correct answer is 33 1/3%. I cannot figure out how.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
S%5B1%5D+=+k%2FT%5B1%5D Solve for T%5B1%5D.
T%5B1%5D+=+k%2FS%5B1%5D
Increase S by 50% to get S%5B2%5D+=+%283%2F2%29S%5B1%5D so now you have:
T%5B2%5D+=+k%2F%283%2F2%29S%5B1%5D Simplify the right side.
T%5B2%5D+=+%282%2F3%29%28k%2FS%5B1%5D%29=%282%2F3%29T%5B1%5D so...
T%5B1%5D has decreased by 1%2F3%29 or 331%2F3%