Final answer:
To find the value of x, we first obtain the total sum of the numbers using their average, then subtract the sum of four given numbers from the total to solve for x. Thus, x equals 4.
Step-by-step explanation:
In this mathematics problem, we have to find the value of x in a set of seven numbers with an average of 8 that are placed in the circles. The condition provided is that the sum of the four numbers in each of two lines is equal to 30.
Let's denote these seven numbers as A, B, C, D, E, F, and G, where one of these represents x. First, we calculate the total sum of the seven numbers using the average: 7 numbers × average (8) = 56. This is because the average is the sum of all the numbers divided by the count of the numbers.
Next, since we are told that the sum of four numbers in any two lines is the same and equal to 30, we have two equalities: A + B + C + D = 30 and E + F + G + x = 30. From these equalities, if we subtract the second from the total sum (56), we can find the value of x as follows: 56 - 30 = 26, which is the sum of A + B + C + D.
To find x, we calculate 30 (the sum of E + F + G + x) minus 26 (the sum of the other numbers), which gives us x = 4.