Solve 20 times (16 - x) equals 12 times (20 - x), for x.

Step-by-step solution

1. 1

   Expand both sides. Each outer factor multiplies both terms in its bracket:

   $20\cdot 16-20x=12\cdot 20-12x\quad\Rightarrow\quad 320-20x=240-12x$

   The two constants happen to be close ($320$ and $240$) while the coefficients differ, which is what makes a single crossing point exist.

2. 2

   Move the $x$ terms to the side that keeps them positive. Adding $20x$ to both sides:

   $320=240+8x$

   The coefficient $8=20-12$ is the difference of the two multipliers.

3. 3

   Move the constants across. Subtract $240$:

   $80=8x$

4. 4

   Divide.

   $x=\frac{80}{8}=10$

5. 5

   Check both sides separately. Left: $20(16-10)=20\cdot 6=120$. Right: $12(20-10)=12\cdot 10=120$. They agree, so $x=10$ — the amount you must remove from $16$ and from $20$ to make the two weighted quantities balance at $120$.