Answer: 2209

Explanation:1. Recall the formula for the area of a circle: Area $A = \pi r^2$, where r is the radius.

2. Calculate the area of circle A ($Area\_A$): Radius of circle A, $r\_A = 2x$. $Area\_A = \pi (r\_A)^2 = \pi (2x)^2 = \pi (4x^2) = 4\pi x^2$.

3. Calculate the area of circle B ($Area\_B$): Radius of circle B, $r\_B = 94x$. $Area\_B = \pi (r\_B)^2 = \pi (94x)^2 = \pi (94^2 x^2)$.

4. Calculate $94^2$: $94^2 = 94 \times 94$. $94 \times 94 = (90+4)(90+4) = 90^2 + 2 \cdot 90 \cdot 4 + 4^2$ $= 8100 + 720 + 16$ $= 8820 + 16 = 8836$. So, $Area\_B = 8836 \pi x^2$.

5. Find how many times the area of circle B is the area of circle A: This means we need to calculate the ratio $\dfrac{Area\_B}{Area\_A}$. $\dfrac{Area\_B}{Area\_A} = \dfrac{8836 \pi x^2}{4 \pi x^2}$

6. Simplify the ratio: The terms $\pi x^2$ cancel out (assuming $x \neq 0$, which is implicit for a radius). Ratio = $\dfrac{8836}{4}$

Perform the division: $8836 \div 4$: $8800 \div 4 = 2200$ $36 \div 4 = 9$ So, $2200 + 9 = 2209$. Ratio = $2209$.

7. Alternative way to find the ratio of areas: The ratio of the areas of two similar figures (circles are always similar) is the square of the ratio of their corresponding linear dimensions (radii in this case). Ratio of radii = $\dfrac{r\_B}{r\_A} = \dfrac{94x}{2x} = \dfrac{94}{2} = 47$. Ratio of areas = $(\text{Ratio of radii})^2 = (47)^2$.

Calculate $47^2$: $47^2 = (50-3)^2 = 50^2 - 2 \cdot 50 \cdot 3 + 3^2$ $= 2500 - 300 + 9$ $= 2200 + 9 = 2209$.

8. Conclusion: The area of circle B is $2209$ times the area of circle A.