SOLUTION: I just got my SAT test book back and there is one problem that I do not know how to do: The product of a and b is equal to x and the sum of a and b is equal to y. If x and y ar

Algebra ->  Conversion and Units of Measurement -> SOLUTION: I just got my SAT test book back and there is one problem that I do not know how to do: The product of a and b is equal to x and the sum of a and b is equal to y. If x and y ar      Log On


   



Question 469796: I just got my SAT test book back and there is one problem that I do not know how to do:
The product of a and b is equal to x and the sum of a and b is equal to y. If x and y are positive numbers, what is 1/a + 1/b in terms of x and y. The answer is y/x but I don't understand how to get that answer. Help!
Thanks.

Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given 1%2Fa+%2B+1%2Fb
Combine this into 1 fraction, find common denominator
common denominator is ab
--> 1%2Fa+%2B+1%2Fb+=+%28b%2Fab%29%2B%28a%2Fab%29+=+%28a%2Bb%29%2Fab
Then use substitution:
we know a+b = y and ab = x
--> %28a%2Bb%29%2Fab+=+y%2Fx