Question

Solve the formula for the variable c.


x/a=b/c

Answer 1

(d) c = ab/x

Explanation:

You want to solve the proportion x/a = b/c for the variable c.

Solution

The usual method recommended for solving almost any kind of proportion is to first clear the fractions. You do this by multiplying both sides by the product of the denominators. This has the appearance of "cross multiplication."

`(x)/(a)=(b)/(c)\qquad\text{given}\\\\\\(x)/(a)\cdot ac=(b)/(c)\cdot ac\qquad\text{multiply by $ac$}\\\\xc=ba\qquad\text{simplify; each numerator times the opposite denominator}`

At this point, it is a "one-step" linear equation in c, so is solved by dividing by the coefficient of c, which is x.

`(xc)/(x)=(ab)/(x)\\\\\boxed{c=(ab)/(x)}`