Solve x times (1 plus 10 percent) equals 518, for x.

Step-by-step solution

1. 1

   Turn the percent into a decimal. $10\%=\frac{10}{100}=0.10$, so the multiplier is

   $1+10\%=1.10$

   and the equation is $1.1x=518$. In words: $x$ is the amount before a $10\%$ increase, and $518$ is the amount after.

2. 2

   Divide by the multiplier.

   $x=\frac{518}{1.10}$

   Note you divide by $1.1$ — not multiply by $0.9$, which would be the classic percentage trap and would give $466.2$.

3. 3

   Clear the decimal to get the exact value. Multiply numerator and denominator by $10$:

   $x=\frac{5180}{11}$

   Since $11\cdot 470=5170$ with remainder $10$, the fraction does not reduce to a whole number: $x=470+\frac{10}{11}$.

4. 4

   Write the decimal. $\frac{10}{11}=0.909090\ldots$, so

   $x=470.909090\ldots\approx 470.9091$

   In a money context this would be rounded to $470.91$.

5. 5

   Reject the round answer 470. Testing it: $1.1\times 470=517$, which is a full unit short of $518$. Testing the correct value: $1.1\times 470.909091=518.000000$ ✓. So $x=\frac{5180}{11}$, not $470$.