The average of x and y is 45, and the average of y and z is 50. If y = 42, then find the value of (x + z).

Question: The average of x and y is 45, and the average of y and z is 50. If y = 42, then find the value of (x + z).

Solution:
Given y = 42

Average of x and y = 45
∴ x + y = 45 × 2
⇒ x + y = 90
⇒ x + 42 = 90
⇒ x = 90 - 42
⇒ x = 48

Average of y and z = 50
∴ y + z = 50 × 2
⇒ y + z = 100
⇒ 42 + z = 100
⇒ z = 100 - 42
⇒ z = 58

Now, x + z = 48 + 58 = 106