Let the three numbers be: X, Y, Z.
The sum of the 3 even numbers is 64.
X + Y + Z = 64 --------------------- (1)
The quotient of 1 more than the second number and 2 less than the first number is 0.5.
(Y + 1) / (X - 2) = 0.5 = 1/2
cross-multiplying,
2Y + 2 = X - 2
2Y = X - 4 ------------------------ (2)
Quotient of 4 more than twice the second number and 2 less than the third number is 2. What are these three numbers?
(2Y + 4) / (Z - 2) = 2
2Y + 4 = 2Z - 4
2Y = 2Z - 8
Y = Z - 4 ------------------------ (3)
Substituting for X = 2Y + 4 from (2) into (1),
2Y + 4 + Y + Z = 64
3Y + Z = 60 -------------------- (4)
Substituting for Y = Z - 4 from (3) into (4),
3Z - 12 + Z = 60
4Z = 72
Z = 18
Using (3), Y = 14
Using X = 2Y + 4 from (2), X = 32
The three numbers are: X = 32, Y = 14, Z = 18