If a number is increased by 84, it becomes 107% of itself. What is that number?

Step 1: Let the number be $x$.
When increased by 84, it becomes 107% of itself.

Step 2: Formula:
$x + 84 = \frac{107}{100} x$

Step 3: Subtract $x$ from both sides:
$84 = \frac{107}{100} x - x$
$84 = \left( \frac{107}{100} - 1 \right) x$
$84 = \frac{7}{100} x$

Step 4: Multiply both sides by $\frac{100}{7}$:
$x = 84 \times \frac{100}{7}$

Step 5: Calculate:
$84 \div 7 = 12$
$12 \times 100 = 1200$
So, $x = 1200$.

Verification:
$1200 + 84 = 1284$
$107\% of 1200 = 1.07 \times 1200 = 1284$
Correct.

Answer: (4) 1200
1200