2200.21 – An Equation with Fractions

Let $x$ represent the target number. Then,

$$\dfrac{x}{3} + \dfrac{x}{10} + \dfrac{x}{12} + 58 = x$$

The least common denominator is 60. To clear fractions, we multiply by it:

$$\begin{align*}20 x + 6 x + 5 x + 58 \cdot 60 &= 60 x \\31 x &= 3480 \\x &= 120\end{align*}$$