Solve the equation 20x + 10x = 1815.

Step-by-step solution

1. 1

   Add the like terms. The two terms share the factor $x$:

   $20x+10x=30x\quad\Longrightarrow\quad 30x=1815$

2. 2

   Divide both sides by $30$.

   $x=\frac{1815}{30}$

3. 3

   Cancel the greatest common divisor. $1815=15\cdot 121$ and $30=15\cdot 2$, so the common factor is $15$:

   $\frac{1815}{30}=\frac{121}{2}$

   Cancelling $5$ first (to $\tfrac{363}{6}$) then $3$ gets to the same place; taking the full gcd in one go is just faster.

4. 4

   Convert to a decimal — here it is exact. Because the reduced denominator is $2$, a power of $10$'s prime factor, the decimal terminates:

   $x=\frac{121}{2}=60.5$

   Contrast with $30x=2000$, whose answer $\tfrac{200}{3}$ never terminates.

5. 5

   Check. $30\times 60.5=1815$ $\checkmark$.