Thread: Find b in x/(x+b) = c

1. Find b in x/(x+b) = c

If x = 5 and c = 0.25, how do I find b in x/(x+b) = c?

2. Re: Find b in x/(x+b) = c

Originally Posted by usc00
If x = 5 and c = 0.25, how do I find b in x/(x+b) = c?

Out of different methods, you may want to experiment with this:

x/(x + b) = c/1

Invert each side:

(x + b)/x = 1/c

x/x + b/x = 1/c

1 + b/x = 1/c

b/x = 1/c - 1

b = x(1/c - 1)

Substitute the values for x and c and simplify the
expression to an integer, or fraction, as appropriate.

3. Re: Find b in x/(x+b) = c

My favorite is criss-cross multiplication;
example: if a/u = b/v then av = bu

With yours:
x/(x+b) = c/1 : x = c(x+b) : x = cx + cb : cb = x - cx : b = x(1-c)/c : same results as greg's

4. Re: Find b in x/(x+b) = c

In addition to greg1313 solution, you can also do this way

x/(x+b) = c

multiply both sides by (x + b)

(x + b)x/(x + b) = c(x + b)

(x + b) on the left side will be cancelled

x = c(x + b)

x = cx + cb

cb = x - cx

b = (x - cx)/c = (5 - (0.25)(5))/0.25 = 15