Solve x divided by (0.33668 + x) equals 0.95, for x.

Step-by-step solution

1. 1

   Recognise the structure. The equation says $x$ makes up $95\%$ of the total $0.33668+x$. So the fixed amount $0.33668$ is the remaining $5\%$, and the answer should be $\frac{95}{5}=19$ times it. Predicting the factor $19$ gives a target to check the algebra against.

2. 2

   Clear the denominator. The denominator is nonzero for any solution, so multiply through:

   $x=0.95(0.33668+x)$

3. 3

   Distribute.

   $x=0.319846+0.95x$

   since $0.95\times 0.33668=0.319846$.

4. 4

   Collect the $x$ terms. Subtract $0.95x$ from both sides:

   $x-0.95x=0.319846\quad\Rightarrow\quad 0.05x=0.319846$

   That coefficient $0.05$ is precisely the $5\%$ that $x$ is not; the smaller it is, the larger $x$ becomes.

5. 5

   Divide and confirm the predicted factor.

   $x=\frac{0.319846}{0.05}=6.39692$

   and indeed $19\times 0.33668=6.39692$, matching step 1 exactly.

6. 6

   Check by substitution. The total is $0.33668+6.39692=6.7336$, and

   $\frac{6.39692}{6.7336}=0.95$

   exactly, so $x=6.39692$.