Final answer:
In the candy distribution problem, we use algebra to create equations from the conditions given and solve for the number of candies each person has. By adding these numbers, we get the total candies.
Step-by-step explanation:
To solve the candy distribution scenario involving three individuals, we will use algebra to set up equations based on the given conditions and solve for the number of candies each individual has.
Let's define the number of candies that a, b, and c have initially as A, B, and C respectively.
From the first condition, if a gives b 20 candies, b's candy count will be twice the sum of a and c's candy counts. This can be written as:
B + 20 = 2(A - 20 + C).
From the second condition, if a gives c 30 candies, c's candy count will be three times the sum of a and b's candy counts. This can be written as:
C + 30 = 3(A - 30 + B).
Solving these equations simultaneously will give us the values for A, B, and C, which we can then add up to find the total number of candies, A + B + C.