Answer:To find the mean of a, b, and c, we first need to determine their individual values.
We can use the two given equations to solve for a, b, and c:
2a + b = 7 (equation 1)
b + 2c = 23 (equation 2)
Solving for b in equation 1, we get:
b = 7 - 2a
Substituting this value of b into equation 2, we get:
7 - 2a + 2c = 23
Simplifying this equation, we get:
2c - 2a = 16
Dividing both sides by 2, we get:
c - a = 8
Solving for c in terms of a, we get:
c = a + 8
Now, we can substitute this expression for c into equation 2 to solve for b:
b + 2c = 23
b + 2(a + 8) = 23
b + 2a + 16 = 23
b + 2a = 7
Substituting the value of b from equation 1 into this equation, we get:
7 - 2a + 2a = 7
Therefore, we have found that:
b = 7 - 2a
c = a + 8
To find the mean of a, b, and c, we can add these values together and divide by 3:
mean = (a + b + c) / 3
Substituting the expressions we found for b and c, we get:
mean = (a + (7 - 2a) + (a + 8)) / 3
Simplifying this equation, we get:
mean = (3a + 15) / 3
mean = a + 5
Therefore, the mean of a, b, and c is equal to a + 5. We do not have enough information to determine the specific values of a, b, and c, so we cannot determine the exact value of the mean.
Explanation: