Mary's thinking of 3 consecutive even integers, X, Y, and Z. 3 times the value of Z exceeds half the value of X by 37. What's the value of Z

Answer: The value of Z is 14

Step-by-step explanation: The numbers are X, Y and Z and they are described as consecutive integers. That means there is a difference of 2 between each number (just like even numbers 2, 4, 6 8 ...). In other words if the first number is X, the next number would be X+2, while the third one would be X+4, and so on. This means Y would be X+2 and Z would be X+4.

However, 3 times the value of Z (X+4) exceeds half of X (X/2) by 37. This can be expressed as follows;

3 (X + 4) = X/2 + 37

3X + 12 = X/2 + 37

3X - X/2 = 37 - 12

(6X - X) / 2 = 25

6X - X = 25 * 2

5X = 50

Divide both sides of the equation by 5

X = 10

Therefore, Z (X + 4) equals 10 + 4 which gives you 14

The value of Z = 14