Correct Option (B)
Let R represent the number of red balls, Y the number of yellow balls, and G the number of green balls.
According to the problem statement:
- "There are as many red balls as there are yellow balls." This translates to the equation: R = Y.
- "There are twice as many yellow balls as there are green ones." This translates to the equation: Y = 2G.
By substituting the second equation (Y = 2G) into the first equation (R = Y), we derive the relationship: R = 2G.
Therefore, the number of red balls is double the number of green balls.
Incorrect Options:
The fundamental relationships established are R = Y and Y = 2G, which implies R = 2G.
Option (A): is equal to the sum of yellow and green balls.
The sum of yellow and green balls is Y + G. Since Y = 2G, this sum becomes 2G + G = 3G. As R = 2G, R is not equal to 3G. Hence, this option is incorrect.
Option (C): is equal to yellow balls minus green balls.
Yellow balls minus green balls is Y - G. Since Y = 2G, this difference becomes 2G - G = G. As R = 2G, R is not equal to G. Hence, this option is incorrect.
Option (D): cannot be ascertained.
The given conditions provide sufficient information to establish a direct and definite relationship between the number of red balls and green balls (R = 2G). Therefore, the number of red balls can be ascertained in relation to the number of green balls. Hence, this option is incorrect.